\usepackage or this document’s own macros. Corpus-wide, \bm occurs 327 times, \Perp is defined by no package and spans 10 documents, and 11,088 of 11,624 undefined occurrences are the source document’s own macros. A row that looks wrong here may be correct, and one that looks right here may not compile. The LaTeX report renders through the document’s own preamble and is the surface to judge from.2477 rows
The page, the confidence and the picture of an inline formula are its HOST LINE's --- a formula has none of its own. A line's confidence is not a formula's.
| Identifier | Page | Conf. | LaTeX source | Rendered | Image |
|---|---|---|---|---|---|
| voloshin-hypergraph_FO0001 | 87 | 1.000 | K_{5} | | |
| voloshin-hypergraph_FO0002 | 87 | 1.000 | K_{3,3} | | |
| voloshin-hypergraph_FO0003 | 15 | 0.994 | \Rightarrow | | |
| voloshin-hypergraph_FO0004 | 21 | 0.999 | A, B, \ldots | | |
| voloshin-hypergraph_FO0005 | 21 | 1.000 | X, Y, Z | | |
| voloshin-hypergraph_FO0006 | 21 | 1.000 | a, b, \ldots, e, \ldots, x, y, z | | |
| voloshin-hypergraph_FO0007 | 22 | 1.000 | G=(X, E) | | |
| voloshin-hypergraph_FO0008 | 22 | 1.000 | A | | |
| voloshin-hypergraph_FO0009 | 22 | 1.000 | |A| | | |
| voloshin-hypergraph_FO0010 | 22 | 0.883 | \boldsymbol{\emptyset} | | |
| voloshin-hypergraph_FO0011 | 22 | 0.967 | X | | |
| voloshin-hypergraph_FO0012 | 22 | 0.967 | X=\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} | | |
| voloshin-hypergraph_FO0013 | 22 | 0.971 | x_{i} | | |
| voloshin-hypergraph_FO0014 | 22 | 0.971 | i | | |
| voloshin-hypergraph_FO0015 | 22 | 0.971 | n | | |
| voloshin-hypergraph_FO0016 | 22 | 0.971 | E | | |
| voloshin-hypergraph_FO0017 | 22 | 0.996 | E=\left\{e_{1}, e_{2}, \ldots, e_{m}\right\} | | |
| voloshin-hypergraph_FO0018 | 22 | 0.996 | e_{i} | | |
| voloshin-hypergraph_FO0019 | 22 | 0.996 | m | | |
| voloshin-hypergraph_FO0020 | 22 | 1.000 | G | | |
| voloshin-hypergraph_FO0021 | 22 | 1.000 | n=5 | | |
| voloshin-hypergraph_FO0023 | 22 | 1.000 | X=\left\{x_{1}, x_{2}, x_{3}, x_{4}, x_{5}\right\} | | |
| voloshin-hypergraph_FO0029 | 22 | 1.000 | x_{1} | | |
| voloshin-hypergraph_FO0030 | 22 | 1.000 | x_{2} | | |
| voloshin-hypergraph_FO0031 | 22 | 1.000 | x_{3} | | |
| voloshin-hypergraph_FO0032 | 22 | 1.000 | x | | |
| voloshin-hypergraph_FO0033 | 22 | 1.000 | d(x) | | |
| voloshin-hypergraph_FO0035 | 22 | 1.000 | \Delta(G) | | |
| voloshin-hypergraph_FO0037 | 23 | 1.000 | N(x) | | |
| voloshin-hypergraph_FO0038 | 23 | 1.000 | N\left(x_{1}\right)=\left\{x_{2}, x_{5}\right\} | | |
| voloshin-hypergraph_FO0039 | 23 | 1.000 | d\left(x_{1}\right)=\left|N\left(x_{1}\right)\right|=2 | | |
| voloshin-hypergraph_FO0040 | 23 | 1.000 | d\left(x_{2}\right)=\left|N\left(x_{2}\right)\right|=4 | | |
| voloshin-hypergraph_FO0041 | 23 | 1.000 | e_{1} | | |
| voloshin-hypergraph_FO0042 | 23 | 1.000 | e_{2} | | |
| voloshin-hypergraph_FO0043 | 23 | 1.000 | e_{3} | | |
| voloshin-hypergraph_FO0044 | 23 | 1.000 | e | | |
| voloshin-hypergraph_FO0045 | 23 | 1.000 | x_{5} | | |
| voloshin-hypergraph_FO0046 | 23 | 1.000 | V(G) | | |
| voloshin-hypergraph_FO0047 | 23 | 1.000 | E(G) | | |
| voloshin-hypergraph_FO0048 | 23 | 1.000 | G=(V(G), E(G)) | | |
| voloshin-hypergraph_FO0049 | 23 | 1.000 | n=n(G) | | |
| voloshin-hypergraph_FO0050 | 23 | 1.000 | m=m(G) | | |
| voloshin-hypergraph_FO0051 | 23 | 1.000 | E(x) | | |
| voloshin-hypergraph_FO0052 | 23 | 1.000 | V(G)=X=\left\{x_{1}, x_{2}, x_{3}, x_{4}, x_{5}\right\},|X|=n=5 | | |
| voloshin-hypergraph_FO0053 | 23 | 0.803 | E(G)=E=\left\{\left\{x_{1}, x_{2}\right\},\left\{x_{2}, x_{3}\right\},\left\{x_{3}, x_{4}\right\},\left\{x_{4}, x_{5}\right\},\left\{x_{5}, x_{1}\right\},\left\{x_{2}, x_{5}\right\},\left\{x_{2}, x_{4}\right\}\right\},|E|=m=7 | | |
| voloshin-hypergraph_FO0054 | 23 | 1.000 | E\left(x_{1}\right)=\left\{e_{1}, e_{5}\right\} | | |
| voloshin-hypergraph_FO0056 | 23 | 1.000 | n-1 | | |
| voloshin-hypergraph_FO0057 | 23 | 1.000 | 0 \leq d(x) \leq n-1 | | |
| voloshin-hypergraph_FO0058 | 23 | 0.998 | n-1.0 | | |
| voloshin-hypergraph_FO0059 | 23 | 1.000 | d\left(x_{1}\right)=d\left(x_{3}\right)=2 | | |
| voloshin-hypergraph_FO0060 | 23 | 1.000 | d\left(x_{4}\right)=d\left(x_{5}\right)=3 | | |
| voloshin-hypergraph_FO0061 | 24 | 1.000 | G_{1}, G_{2} | | |
| voloshin-hypergraph_FO0062 | 24 | 1.000 | G_{3} | | |
| voloshin-hypergraph_FO0063 | 24 | 0.999 | x_{1}, x_{2}, x_{3}, x_{4} | | |
| voloshin-hypergraph_FO0064 | 25 | 1.000 | x_{4} | | |
| voloshin-hypergraph_FO0065 | 25 | 1.000 | \left\{x_{1}\right\},\left\{x_{2}\right\},\left\{x_{3}\right\} | | |
| voloshin-hypergraph_FO0066 | 25 | 1.000 | \left\{x_{4}\right\},\left\{x_{5}\right\} | | |
| voloshin-hypergraph_FO0067 | 25 | 1.000 | \left\{x_{1}, x_{3}\right\},\left\{x_{2}\right\},\left\{x_{4}\right\},\left\{x_{5}\right\} | | |
| voloshin-hypergraph_FO0068 | 25 | 1.000 | \left\{x_{1}, x_{4}\right\},\left\{x_{2}\right\},\left\{x_{3}, x_{5}\right\} | | |
| voloshin-hypergraph_FO0069 | 25 | 1.000 | x_{1}, x_{2} | | |
| voloshin-hypergraph_FO0070 | 25 | 1.000 | \left\{x_{1}, x_{3}\right\} | | |
| voloshin-hypergraph_FO0071 | 25 | 0.993 | \left\{x_{2}, x_{4}\right\} | | |
| voloshin-hypergraph_FO0072 | 25 | 0.993 | \left\{x_{5}\right\} | | |
| voloshin-hypergraph_FO0073 | 28 | 0.982 | x_{1}: x_{2}, x_{5} | | |
| voloshin-hypergraph_FO0074 | 28 | 0.990 | x_{2}: x_{1}, x_{3}, x_{4}, x_{5} | | |
| voloshin-hypergraph_FO0075 | 28 | 0.919 | x_{3}: x_{2}, x_{4} | | |
| voloshin-hypergraph_FO0076 | 28 | 0.999 | x_{4}: x_{2}, x_{3}, x_{5} | | |
| voloshin-hypergraph_FO0077 | 28 | 0.996 | x_{5}: x_{1}, x_{2}, x_{4} | | |
| voloshin-hypergraph_FO0078 | 29 | 1.000 | L(G) | | |
| voloshin-hypergraph_FO0079 | 29 | 1.000 | x_{j} | | |
| voloshin-hypergraph_FO0080 | 29 | 1.000 | (i, j) | | |
| voloshin-hypergraph_FO0081 | 29 | 1.000 | A(G) | | |
| voloshin-hypergraph_FO0082 | 29 | 1.000 | A^{\prime} | | |
| voloshin-hypergraph_FO0083 | 29 | 1.000 | A=A^{\prime} | | |
| voloshin-hypergraph_FO0084 | 30 | 1.000 | e_{j} | | |
| voloshin-hypergraph_FO0085 | 30 | 0.789 | I(G) | | |
| voloshin-hypergraph_FO0086 | 30 | 0.910 | I | | |
| voloshin-hypergraph_FO0087 | 30 | 1.000 | J(G) | | |
| voloshin-hypergraph_FO0088 | 31 | 1.000 | \{a, b\}=\{b, a\} | | |
| voloshin-hypergraph_FO0089 | 32 | 0.677 | \{ | | |
| voloshin-hypergraph_FO0090 | 32 | 0.677 | \} , one use parentheses (,). So now (a, b) \neq(b, a) | | |
| voloshin-hypergraph_FO0091 | 32 | 0.984 | (x, y) | | |
| voloshin-hypergraph_FO0092 | 32 | 1.000 | y | | |
| voloshin-hypergraph_FO0093 | 32 | 1.000 | L | | |
| voloshin-hypergraph_FO0094 | 32 | 1.000 | J | | |
| voloshin-hypergraph_FO0095 | 33 | 0.546 | a, b, c, d, e, f | | |
| voloshin-hypergraph_FO0096 | 33 | 0.889 | d | | |
| voloshin-hypergraph_FO0097 | 33 | 0.512 | \left(x_{i}, x_{j}\right) | | |
| voloshin-hypergraph_FO0098 | 34 | 1.000 | E_{n} | | |
| voloshin-hypergraph_FO0099 | 34 | 1.000 | E_{4} | | |
| voloshin-hypergraph_FO0100 | 34 | 0.977 | \emptyset | | |
| voloshin-hypergraph_FO0101 | 34 | 0.736 | P_{5} | | |
| voloshin-hypergraph_FO0102 | 34 | 0.994 | x_{1}, x_{2}, \ldots, x_{n} | | |
| voloshin-hypergraph_FO0103 | 34 | 1.000 | P_{n} | | |
| voloshin-hypergraph_FO0104 | 34 | 1.000 | m=n-1 | | |
| voloshin-hypergraph_FO0105 | 34 | 1.000 | P_{2} | | |
| voloshin-hypergraph_FO0106 | 34 | 1.000 | x_{n} | | |
| voloshin-hypergraph_FO0107 | 34 | 0.736 | \left(x_{1}, x_{5}\right) | | |
| voloshin-hypergraph_FO0108 | 35 | 1.000 | G_{1} | | |
| voloshin-hypergraph_FO0109 | 35 | 1.000 | G_{2} | | |
| voloshin-hypergraph_FO0110 | 35 | 1.000 | G^{\prime} | | |
| voloshin-hypergraph_FO0111 | 35 | 1.000 | k | | |
| voloshin-hypergraph_FO0112 | 35 | 1.000 | G=k G^{\prime} | | |
| voloshin-hypergraph_FO0113 | 35 | 1.000 | C_{n} | | |
| voloshin-hypergraph_FO0115 | 46 | 0.798 | C_{6} | | |
| voloshin-hypergraph_FO0116 | 35 | 1.000 | C_{1} | | |
| voloshin-hypergraph_FO0117 | 35 | 1.000 | C_{2} | | |
| voloshin-hypergraph_FO0118 | 35 | 1.000 | C_{3} | | |
| voloshin-hypergraph_FO0119 | 36 | 1.000 | W_{6} | | |
| voloshin-hypergraph_FO0120 | 35 | 1.000 | C_{k}, k \geq 3 | | |
| voloshin-hypergraph_FO0121 | 36 | 1.000 | C_{k} | | |
| voloshin-hypergraph_FO0122 | 36 | 1.000 | W_{k+1} | | |
| voloshin-hypergraph_FO0123 | 36 | 1.000 | K_{n} | | |
| voloshin-hypergraph_FO0124 | 36 | 1.000 | n \geq 1 | | |
| voloshin-hypergraph_FO0125 | 36 | 1.000 | K_{1}, K_{2}, K_{3}, K_{4}, K_{5} | | |
| voloshin-hypergraph_FO0126 | 36 | 1.000 | K_{6} | | |
| voloshin-hypergraph_FO0127 | 36 | 1.000 | n(n-1)=2 m | | |
| voloshin-hypergraph_FO0128 | 36 | 1.000 | m=6(6-1) / 2=15 | | |
| voloshin-hypergraph_FO0129 | 36 | 1.000 | K_{2}= | | |
| voloshin-hypergraph_FO0130 | 36 | 1.000 | P_{2}, K_{3}=C_{3} | | |
| voloshin-hypergraph_FO0131 | 36 | 1.000 | K_{4}=W_{4} | | |
| voloshin-hypergraph_FO0132 | 36 | 1.000 | T_{n} | | |
| voloshin-hypergraph_FO0133 | 36 | 1.000 | P_{n}, K_{n}, C_{n} | | |
| voloshin-hypergraph_FO0134 | 36 | 1.000 | W_{n} | | |
| voloshin-hypergraph_FO0135 | 36 | 1.000 | P_{4} | | |
| voloshin-hypergraph_FO0136 | 37 | 1.000 | X_{1} | | |
| voloshin-hypergraph_FO0137 | 37 | 1.000 | X_{2} | | |
| voloshin-hypergraph_FO0138 | 37 | 1.000 | G=\left(X_{1}, X_{2} ; E\right) | | |
| voloshin-hypergraph_FO0139 | 37 | 1.000 | \left|X_{1}\right|=r | | |
| voloshin-hypergraph_FO0140 | 37 | 0.987 | \left|X_{2}\right|=s | | |
| voloshin-hypergraph_FO0141 | 37 | 0.987 | K_{r, s} | | |
| voloshin-hypergraph_FO0142 | 37 | 1.000 | r s | | |
| voloshin-hypergraph_FO0143 | 37 | 0.999 | K_{1,3} | | |
| voloshin-hypergraph_FO0144 | 37 | 0.999 | C_{4} | | |
| voloshin-hypergraph_FO0145 | 37 | 0.999 | X_{1}, X_{2} | | |
| voloshin-hypergraph_FO0146 | 37 | 0.998 | (n-1) | | |
| voloshin-hypergraph_FO0147 | 38 | 0.999 | C_{5} | | |
| voloshin-hypergraph_FO0148 | 39 | 1.000 | G_{1}=\left(X_{1}, E_{1}\right) | | |
| voloshin-hypergraph_FO0149 | 39 | 1.000 | G_{2}=\left(X_{2}, E_{2}\right) | | |
| voloshin-hypergraph_FO0150 | 39 | 1.000 | G_{1} \cong G_{2} | | |
| voloshin-hypergraph_FO0151 | 39 | 0.999 | \left|X_{1}\right|=\left|X_{2}\right|=n | | |
| voloshin-hypergraph_FO0152 | 39 | 1.000 | n-2 | | |
| voloshin-hypergraph_FO0153 | 39 | 1.000 | n(n-1)(n- | | |
| voloshin-hypergraph_FO0154 | 39 | 0.979 | 2) \cdots 3 \cdot 2 \cdot 1=n! | | |
| voloshin-hypergraph_FO0155 | 39 | 0.979 | n! | | |
| voloshin-hypergraph_FO0156 | 39 | 0.990 | 1,2, \ldots n! | | |
| voloshin-hypergraph_FO0157 | 39 | 0.840 | 2 n | | |
| voloshin-hypergraph_FO0158 | 39 | 1.000 | T_{1} | | |
| voloshin-hypergraph_FO0159 | 39 | 1.000 | T_{2} | | |
| voloshin-hypergraph_FO0160 | 39 | 1.000 | 8!=40320 | | |
| voloshin-hypergraph_FO0161 | 40 | 1.000 | \boldsymbol{\sigma} | | |
| voloshin-hypergraph_FO0162 | 40 | 1.000 | a | | |
| voloshin-hypergraph_FO0163 | 40 | 1.000 | b | | |
| voloshin-hypergraph_FO0164 | 40 | 0.665 | \binom{6}{2}=15 | | |
| voloshin-hypergraph_FO0165 | 40 | 0.665 | 6!=720 | | |
| voloshin-hypergraph_FO0166 | 40 | 1.000 | E_{n}, K_{n}, C_{n}, W_{n} | | |
| voloshin-hypergraph_FO0167 | 40 | 0.987 | r | | |
| voloshin-hypergraph_FO0168 | 40 | 0.987 | s, 1 \leq r, s \leq 5 | | |
| voloshin-hypergraph_FO0169 | 40 | 1.000 | K_{s, r} | | |
| voloshin-hypergraph_FO0170 | 41 | 1.000 | L(G), A(G), I(G), J(G) | | |
| voloshin-hypergraph_FO0171 | 41 | 1.000 | L\left(G_{1}\right), A\left(G_{1}\right), I\left(G_{1}\right) | | |
| voloshin-hypergraph_FO0172 | 41 | 1.000 | J\left(G_{1}\right) | | |
| voloshin-hypergraph_FO0173 | 41 | 1.000 | L\left(G_{2}\right), A\left(G_{2}\right), I\left(G_{2}\right) | | |
| voloshin-hypergraph_FO0174 | 41 | 1.000 | J\left(G_{2}\right) | | |
| voloshin-hypergraph_FO0175 | 41 | 1.000 | \sigma | | |
| voloshin-hypergraph_FO0176 | 41 | 1.000 | x \in X | | |
| voloshin-hypergraph_FO0177 | 41 | 0.977 | X_{1}=X-\{x\} | | |
| voloshin-hypergraph_FO0178 | 41 | 1.000 | E_{1}=E-E(x) | | |
| voloshin-hypergraph_FO0179 | 42 | 1.000 | G_{1}=G-x | | |
| voloshin-hypergraph_FO0180 | 42 | 1.000 | E(x)=\left\{e_{1}, e_{2}, e_{3}\right\} | | |
| voloshin-hypergraph_FO0181 | 42 | 1.000 | G_{1}=G-e_{3} | | |
| voloshin-hypergraph_FO0182 | 43 | 1.000 | e=\{x, y\} \in E | | |
| voloshin-hypergraph_FO0183 | 43 | 1.000 | x y | | |
| voloshin-hypergraph_FO0184 | 44 | 0.926 | N(x) \cap N(y) \neq \emptyset | | |
| voloshin-hypergraph_FO0185 | 44 | 0.926 | N(x) \cap N(y) | | |
| voloshin-hypergraph_FO0186 | 44 | 1.000 | e^{\prime} | | |
| voloshin-hypergraph_FO0188 | 44 | 1.000 | C_{k}, k \geq 4 | | |
| voloshin-hypergraph_FO0189 | 44 | 1.000 | C_{3}=K_{3} | | |
| voloshin-hypergraph_FO0190 | 44 | 1.000 | K_{2} | | |
| voloshin-hypergraph_FO0191 | 44 | 1.000 | K_{m} | | |
| voloshin-hypergraph_FO0192 | 44 | 1.000 | n \geq m | | |
| voloshin-hypergraph_FO0193 | 44 | 1.000 | K_{4} | | |
| voloshin-hypergraph_FO0194 | 44 | 1.000 | K_{3} | | |
| voloshin-hypergraph_FO0195 | 44 | 1.000 | \eta(G) | | |
| voloshin-hypergraph_FO0196 | 44 | 1.000 | |X|=n | | |
| voloshin-hypergraph_FO0197 | 44 | 1.000 | \bar{G} | | |
| voloshin-hypergraph_FO0198 | 44 | 1.000 | \bar{G}=\left(X, E^{\prime}\right) | | |
| voloshin-hypergraph_FO0199 | 44 | 1.000 | E^{\prime} | | |
| voloshin-hypergraph_FO0200 | 44 | 1.000 | E \cup E^{\prime} | | |
| voloshin-hypergraph_FO0201 | 44 | 1.000 | \overline{\bar{G}}=G, \bar{E}_{n}=K_{n} | | |
| voloshin-hypergraph_FO0202 | 44 | 1.000 | \bar{K}_{n}=E_{n} | | |
| voloshin-hypergraph_FO0203 | 44 | 1.000 | \overline{P_{4}}, C_{5} | | |
| voloshin-hypergraph_FO0204 | 44 | 1.000 | \overline{C_{5}} | | |
| voloshin-hypergraph_FO0205 | 44 | 1.000 | \overline{K_{r, s}}=\left\{K_{r}, K_{s}\right\} | | |
| voloshin-hypergraph_FO0206 | 45 | 1.000 | C_{4}, W_{5}, K_{5}, K_{3,3} | | |
| voloshin-hypergraph_FO0207 | 45 | 1.000 | C_{5}, W_{5}, K_{2,3} | | |
| voloshin-hypergraph_FO0208 | 45 | 1.000 | C_{3}, C_{4}, C_{5}, C_{6}, K_{5}, K_{3,5} | | |
| voloshin-hypergraph_FO0209 | 45 | 1.000 | P_{7} | | |
| voloshin-hypergraph_FO0210 | 45 | 1.000 | E_{5}, 2 C_{3} | | |
| voloshin-hypergraph_FO0211 | 45 | 0.999 | \bar{C}_{5} \cong C_{5} | | |
| voloshin-hypergraph_FO0212 | 45 | 1.000 | \bar{C}_{6} | | |
| voloshin-hypergraph_FO0213 | 45 | 1.000 | G^{\prime}=\left(X^{\prime}, E^{\prime}\right) | | |
| voloshin-hypergraph_FO0214 | 45 | 1.000 | X^{\prime} \subseteq X | | |
| voloshin-hypergraph_FO0215 | 45 | 1.000 | E^{\prime} \subseteq E | | |
| voloshin-hypergraph_FO0216 | 45 | 1.000 | G^{\prime} \subseteq G | | |
| voloshin-hypergraph_FO0217 | 45 | 1.000 | X^{\prime} | | |
| voloshin-hypergraph_FO0218 | 45 | 1.000 | X-X^{\prime} | | |
| voloshin-hypergraph_FO0219 | 45 | 1.000 | E-E^{\prime} | | |
| voloshin-hypergraph_FO0220 | 45 | 1.000 | \left\{x_{3}, x_{5}\right\} | | |
| voloshin-hypergraph_FO0221 | 46 | 1.000 | Y \subseteq X | | |
| voloshin-hypergraph_FO0222 | 46 | 1.000 | G_{Y} | | |
| voloshin-hypergraph_FO0223 | 46 | 1.000 | k \geq 3 | | |
| voloshin-hypergraph_FO0224 | 46 | 0.996 | x_{2}, x_{3}, x_{4}, x_{5}, x_{2} | | |
| voloshin-hypergraph_FO0225 | 46 | 1.000 | x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{1} | | |
| voloshin-hypergraph_FO0226 | 46 | 1.000 | x_{1}, x_{2}, x_{5}, x_{3}, x_{4}, x_{5}, x_{1} | | |
| voloshin-hypergraph_FO0227 | 46 | 1.000 | K_{1}, K_{2}, K_{3}, \ldots, K_{n} | | |
| voloshin-hypergraph_FO0228 | 46 | 1.000 | K_{r} | | |
| voloshin-hypergraph_FO0229 | 46 | 1.000 | K_{r+1} | | |
| voloshin-hypergraph_FO0230 | 47 | 0.999 | \omega(G) | | |
| voloshin-hypergraph_FO0231 | 47 | 0.998 | G, 1 \leq \omega(G) \leq n | | |
| voloshin-hypergraph_FO0232 | 47 | 1.000 | x_{2}, x_{3}, x_{5} | | |
| voloshin-hypergraph_FO0233 | 47 | 0.958 | \omega(G)=3 | | |
| voloshin-hypergraph_FO0234 | 47 | 0.958 | \omega\left(G_{1}\right)=\omega\left(G_{2}\right)=2 | | |
| voloshin-hypergraph_FO0235 | 47 | 1.000 | E_{1}, E_{2}, \ldots, E_{n} | | |
| voloshin-hypergraph_FO0236 | 47 | 1.000 | E_{k} | | |
| voloshin-hypergraph_FO0237 | 47 | 0.801 | \alpha(G) | | |
| voloshin-hypergraph_FO0238 | 47 | 1.000 | G, 1 \leq \alpha(G) \leq n | | |
| voloshin-hypergraph_FO0239 | 47 | 1.000 | \omega(G)=\alpha(\bar{G}) | | |
| voloshin-hypergraph_FO0240 | 47 | 1.000 | \alpha(G)=\omega(\bar{G}) | | |
| voloshin-hypergraph_FO0241 | 47 | 1.000 | \alpha(G)=2 | | |
| voloshin-hypergraph_FO0242 | 47 | 1.000 | \omega\left(G_{1}\right)=3 | | |
| voloshin-hypergraph_FO0243 | 47 | 1.000 | a, b | | |
| voloshin-hypergraph_FO0244 | 47 | 1.000 | a, b, e | | |
| voloshin-hypergraph_FO0245 | 47 | 1.000 | f | | |
| voloshin-hypergraph_FO0246 | 47 | 0.982 | \alpha\left(G_{2}\right)=4 | | |
| voloshin-hypergraph_FO0247 | 47 | 1.000 | T \subseteq X | | |
| voloshin-hypergraph_FO0248 | 47 | 1.000 | X \backslash T | | |
| voloshin-hypergraph_FO0249 | 47 | 1.000 | T | | |
| voloshin-hypergraph_FO0250 | 47 | 1.000 | \tau(G) | | |
| voloshin-hypergraph_FO0251 | 47 | 1.000 | G=(X, E),|X|=n | | |
| voloshin-hypergraph_FO0252 | 47 | 0.997 | G^{\prime}=\left(X, E^{\prime}\right) | | |
| voloshin-hypergraph_FO0253 | 48 | 0.959 | \{1,2\} | | |
| voloshin-hypergraph_FO0254 | 48 | 0.959 | \{2,3\} | | |
| voloshin-hypergraph_FO0255 | 48 | 0.833 | \nu(G) | | |
| voloshin-hypergraph_FO0256 | 48 | 0.955 | \nu=n / 2 | | |
| voloshin-hypergraph_FO0257 | 48 | 1.000 | \{c, d\} | | |
| voloshin-hypergraph_FO0258 | 48 | 1.000 | \{a, c\} | | |
| voloshin-hypergraph_FO0259 | 48 | 1.000 | \{d, e\} | | |
| voloshin-hypergraph_FO0260 | 48 | 1.000 | \nu\left(G_{2}\right)=2 | | |
| voloshin-hypergraph_FO0261 | 49 | 1.000 | P_{6}, C_{3}, C_{4}, C_{5}, W_{4}, W_{5}, K_{2,3} | | |
| voloshin-hypergraph_FO0262 | 49 | 1.000 | C_{7} | | |
| voloshin-hypergraph_FO0263 | 49 | 1.000 | W_{9} | | |
| voloshin-hypergraph_FO0264 | 49 | 1.000 | K_{4,4} | | |
| voloshin-hypergraph_FO0265 | 49 | 1.000 | K_{6,9} | | |
| voloshin-hypergraph_FO0266 | 49 | 0.939 | v(G) | | |
| voloshin-hypergraph_FO0267 | 49 | 0.999 | \alpha, \omega, \tau | | |
| voloshin-hypergraph_FO0268 | 49 | 0.999 | \nu | | |
| voloshin-hypergraph_FO0269 | 49 | 0.999 | K_{999}, K_{1000}, C_{20}, C_{21}, W_{99}, W_{100}, P_{n}, K_{n}, C_{n}, W_{n} | | |
| voloshin-hypergraph_FO0270 | 49 | 1.000 | n \geq 2 | | |
| voloshin-hypergraph_FO0271 | 49 | 1.000 | W_{5} | | |
| voloshin-hypergraph_FO0272 | 50 | 0.988 | x, y \in X | | |
| voloshin-hypergraph_FO0273 | 50 | 0.999 | \{x, y\} | | |
| voloshin-hypergraph_FO0274 | 50 | 0.999 | S \subseteq X | | |
| voloshin-hypergraph_FO0275 | 50 | 1.000 | S | | |
| voloshin-hypergraph_FO0276 | 50 | 0.448 | \mathrm{k}(G) | | |
| voloshin-hypergraph_FO0277 | 50 | 0.976 | \mathrm{K}\left(K_{n}\right)=n-1 | | |
| voloshin-hypergraph_FO0278 | 50 | 0.530 | G, \mathrm{k}(G) | | |
| voloshin-hypergraph_FO0279 | 50 | 0.953 | \mathrm{K}(G) \geq k | | |
| voloshin-hypergraph_FO0280 | 50 | 0.898 | \mathrm{K}(G) \geq 2 | | |
| voloshin-hypergraph_FO0281 | 50 | 1.000 | (k-1) | | |
| voloshin-hypergraph_FO0282 | 50 | 1.000 | (k-2) | | |
| voloshin-hypergraph_FO0283 | 50 | 1.000 | (k+1) | | |
| voloshin-hypergraph_FO0284 | 51 | 0.865 | \{2,3,5,6\} | | |
| voloshin-hypergraph_FO0287 | 51 | 0.767 | \mathrm{K}(G)=2 | | |
| voloshin-hypergraph_FO0288 | 51 | 1.000 | X_{1} \cup S | | |
| voloshin-hypergraph_FO0289 | 51 | 1.000 | X_{2} \cup S | | |
| voloshin-hypergraph_FO0290 | 51 | 1.000 | G_{X_{1} \cup S} | | |
| voloshin-hypergraph_FO0291 | 51 | 1.000 | G_{X_{2} \cup S} | | |
| voloshin-hypergraph_FO0292 | 51 | 1.000 | x \in S | | |
| voloshin-hypergraph_FO0293 | 51 | 1.000 | S-\{x\} | | |
| voloshin-hypergraph_FO0294 | 52 | 0.965 | \{3,4\} | | |
| voloshin-hypergraph_FO0295 | 52 | 0.695 | \{1,6\} | | |
| voloshin-hypergraph_FO0296 | 52 | 1.000 | k \geq 2 | | |
| voloshin-hypergraph_FO0297 | 52 | 1.000 | X_{1}, X_{2}, \ldots, X_{k} | | |
| voloshin-hypergraph_FO0298 | 52 | 1.000 | G_{1}=G_{X_{1} \cup S}, G_{2}=G_{X_{2} \cup S}, \ldots | | |
| voloshin-hypergraph_FO0299 | 52 | 1.000 | G_{k}=G_{X_{k} \cup S} | | |
| voloshin-hypergraph_FO0300 | 53 | 0.822 | x, y | | |
| voloshin-hypergraph_FO0301 | 53 | 0.783 | \mathbf{K}(G) | | |
| voloshin-hypergraph_FO0302 | 53 | 1.000 | k \geq 0 | | |
| voloshin-hypergraph_FO0303 | 53 | 1.000 | \{1,3,4,7,8\} | | |
| voloshin-hypergraph_FO0304 | 53 | 1.000 | \{1,8,3,4,6\} | | |
| voloshin-hypergraph_FO0305 | 53 | 1.000 | \{5,6,7,8,2\} | | |
| voloshin-hypergraph_FO0306 | 55 | 1.000 | m(G)=n(G)-1 | | |
| voloshin-hypergraph_FO0307 | 55 | 1.000 | 1 . \Rightarrow 2 . G | | |
| voloshin-hypergraph_FO0308 | 55 | 1.000 | n=1,2 | | |
| voloshin-hypergraph_FO0309 | 55 | 1.000 | n(G)>2 | | |
| voloshin-hypergraph_FO0310 | 55 | 1.000 | m\left(G_{1}\right)=n\left(G_{1}\right)-1 | | |
| voloshin-hypergraph_FO0311 | 55 | 1.000 | m(G)=m\left(G_{1}\right)+1 | | |
| voloshin-hypergraph_FO0312 | 55 | 1.000 | n(G)=n\left(G_{1}\right)+1 | | |
| voloshin-hypergraph_FO0313 | 55 | 1.000 | e=\{x, y\} | | |
| voloshin-hypergraph_FO0314 | 55 | 1.000 | G-e | | |
| voloshin-hypergraph_FO0315 | 55 | 0.882 | \Rightarrow 2 . m=n-1 | | |
| voloshin-hypergraph_FO0316 | 55 | 0.999 | k>1 | | |
| voloshin-hypergraph_FO0317 | 55 | 0.999 | G_{1}, G_{2}, \ldots, G_{k} | | |
| voloshin-hypergraph_FO0318 | 55 | 0.999 | G_{i} | | |
| voloshin-hypergraph_FO0319 | 55 | 0.999 | 1 . \Rightarrow 2 . m_{i}=n_{i}-1 | | |
| voloshin-hypergraph_FO0320 | 55 | 0.965 | m(G)=m_{1}+m_{2}+\cdots+m_{k}=\left(n_{1}-1\right)+\left(n_{2}-1\right)+\cdots+\left(n_{k}-1\right)=n-k | | |
| voloshin-hypergraph_FO0321 | 55 | 1.000 | m=n-1=n-k | | |
| voloshin-hypergraph_FO0322 | 55 | 1.000 | k=1 | | |
| voloshin-hypergraph_FO0323 | 56 | 0.996 | C_{l} | | |
| voloshin-hypergraph_FO0324 | 56 | 0.996 | \left(C_{k} \cup C_{l}\right)-\{x, y\} | | |
| voloshin-hypergraph_FO0325 | 56 | 1.000 | \Lambda(G)=m(G)- | | |
| voloshin-hypergraph_FO0326 | 56 | 0.516 | n(G)+k | | |
| voloshin-hypergraph_FO0327 | 56 | 0.516 | \wedge= | | |
| voloshin-hypergraph_FO0328 | 56 | 1.000 | m-n+1=m-(n-1) | | |
| voloshin-hypergraph_FO0329 | 56 | 1.000 | m-(n-1) | | |
| voloshin-hypergraph_FO0330 | 56 | 0.743 | \Lambda | | |
| voloshin-hypergraph_FO0331 | 56 | 0.535 | \wedge(G)=0 | | |
| voloshin-hypergraph_FO0332 | 56 | 0.979 | \Lambda(G)= | | |
| voloshin-hypergraph_FO0333 | 56 | 1.000 | m-n+1=7-5+1=3 | | |
| voloshin-hypergraph_FO0334 | 56 | 1.000 | n^{n-2} | | |
| voloshin-hypergraph_FO0335 | 57 | 1.000 | n=3 | | |
| voloshin-hypergraph_FO0336 | 57 | 1.000 | E_{n}, C_{n}, K_{n}, W_{n} | | |
| voloshin-hypergraph_FO0337 | 57 | 1.000 | C_{6}, K_{4}, W_{6} | | |
| voloshin-hypergraph_FO0338 | 57 | 1.000 | K_{n}, W_{n}, n \geq 5 | | |
| voloshin-hypergraph_FO0339 | 57 | 1.000 | d(x, y) | | |
| voloshin-hypergraph_FO0340 | 57 | 0.731 | d(x, y)=\infty | | |
| voloshin-hypergraph_FO0341 | 57 | 1.000 | d(x, Y)=\min _{y \in Y} d(x, y) | | |
| voloshin-hypergraph_FO0342 | 57 | 1.000 | Y | | |
| voloshin-hypergraph_FO0343 | 57 | 1.000 | x, y, z \in X | | |
| voloshin-hypergraph_FO0344 | 57 | 1.000 | d(x, y) \geq 0 | | |
| voloshin-hypergraph_FO0345 | 57 | 1.000 | d(x, x)=0 | | |
| voloshin-hypergraph_FO0346 | 57 | 1.000 | d(x, y)=d(y, x) | | |
| voloshin-hypergraph_FO0347 | 57 | 1.000 | d(x, y) \leq d(x, z)+d(z, y) | | |
| voloshin-hypergraph_FO0348 | 57 | 0.999 | \operatorname{diam}(G) | | |
| voloshin-hypergraph_FO0349 | 57 | 0.999 | \max _{x, y \in X} d(x, y) | | |
| voloshin-hypergraph_FO0350 | 57 | 0.876 | d(x, y)=\operatorname{diam}(G) | | |
| voloshin-hypergraph_FO0351 | 57 | 1.000 | N_{\infty}(x) | | |
| voloshin-hypergraph_FO0352 | 57 | 1.000 | y \in N_{\infty}(x) | | |
| voloshin-hypergraph_FO0353 | 57 | 1.000 | z \notin N_{\infty}(x) | | |
| voloshin-hypergraph_FO0354 | 57 | 1.000 | d(x, z)<d(x, y) | | |
| voloshin-hypergraph_FO0355 | 58 | 1.000 | z | | |
| voloshin-hypergraph_FO0358 | 58 | 0.570 | d(x, y)=\operatorname{diam}(T) | | |
| voloshin-hypergraph_FO0359 | 58 | 0.570 | x \in N_{\infty}(y) | | |
| voloshin-hypergraph_FO0360 | 58 | 1.000 | K_{1} | | |
| voloshin-hypergraph_FO0361 | 58 | 0.998 | T_{1}, T_{2}, T_{3}, \ldots | | |
| voloshin-hypergraph_FO0362 | 58 | 0.941 | \operatorname{diam}(T) | | |
| voloshin-hypergraph_FO0363 | 58 | 0.991 | x \in N_{\infty}(z) | | |
| voloshin-hypergraph_FO0364 | 58 | 0.991 | y \in N_{\infty}(x): \operatorname{diam}(T)=d(x, y) | | |
| voloshin-hypergraph_FO0365 | 59 | 1.000 | \mathcal{D} | | |
| voloshin-hypergraph_FO0366 | 59 | 1.000 | D | | |
| voloshin-hypergraph_FO0367 | 59 | 1.000 | G=(X, \mathcal{D}) | | |
| voloshin-hypergraph_FO0368 | 59 | 1.000 | D \in \mathcal{D} | | |
| voloshin-hypergraph_FO0369 | 59 | 1.000 | w(D) | | |
| voloshin-hypergraph_FO0370 | 59 | 1.000 | T=(X, E) | | |
| voloshin-hypergraph_FO0371 | 59 | 1.000 | w(T) | | |
| voloshin-hypergraph_FO0372 | 60 | 0.991 | T^{*} \neq T | | |
| voloshin-hypergraph_FO0373 | 60 | 1.000 | w\left(T^{*}\right)<w(T) | | |
| voloshin-hypergraph_FO0374 | 60 | 1.000 | T^{*} | | |
| voloshin-hypergraph_FO0375 | 60 | 1.000 | D^{\prime} | | |
| voloshin-hypergraph_FO0376 | 60 | 1.000 | T^{*}+D-D^{\prime} | | |
| voloshin-hypergraph_FO0377 | 60 | 1.000 | w(D) \leq w\left(D^{\prime}\right) | | |
| voloshin-hypergraph_FO0378 | 60 | 1.000 | w\left(T^{*}+D-D^{\prime}\right)=w\left(T^{*}\right)+ | | |
| voloshin-hypergraph_FO0379 | 60 | 1.000 | w(D)-w\left(D^{\prime}\right) \leq w\left(T^{*}\right) | | |
| voloshin-hypergraph_FO0380 | 60 | 1.000 | w>0 | | |
| voloshin-hypergraph_FO0381 | 61 | 0.973 | B | | |
| voloshin-hypergraph_FO0382 | 61 | 1.000 | x \in A | | |
| voloshin-hypergraph_FO0383 | 61 | 1.000 | x, k | | |
| voloshin-hypergraph_FO0384 | 61 | 0.999 | \{x\} | | |
| voloshin-hypergraph_FO0385 | 61 | 0.999 | N_{0} | | |
| voloshin-hypergraph_FO0386 | 61 | 0.999 | N_{1} | | |
| voloshin-hypergraph_FO0387 | 61 | 0.994 | N_{2} | | |
| voloshin-hypergraph_FO0388 | 61 | 0.994 | N_{3} | | |
| voloshin-hypergraph_FO0389 | 61 | 1.000 | N_{k} | | |
| voloshin-hypergraph_FO0390 | 61 | 0.979 | N_{i} \cap N_{j}=\emptyset, i \neq j | | |
| voloshin-hypergraph_FO0391 | 61 | 1.000 | N_{i} | | |
| voloshin-hypergraph_FO0392 | 61 | 1.000 | X=A \cup B | | |
| voloshin-hypergraph_FO0393 | 61 | 1.000 | e=\{y, z\} | | |
| voloshin-hypergraph_FO0394 | 61 | 1.000 | y, z \in N_{i} | | |
| voloshin-hypergraph_FO0395 | 61 | 0.926 | i>0 | | |
| voloshin-hypergraph_FO0396 | 61 | 0.926 | (x, z) | | |
| voloshin-hypergraph_FO0397 | 61 | 1.000 | x^{\prime} | | |
| voloshin-hypergraph_FO0398 | 61 | 1.000 | \left(x^{\prime}, y\right) | | |
| voloshin-hypergraph_FO0399 | 61 | 1.000 | \left(x^{\prime}, z\right) | | |
| voloshin-hypergraph_FO0400 | 61 | 1.000 | l | | |
| voloshin-hypergraph_FO0401 | 61 | 1.000 | C_{2 l+1} | | |
| voloshin-hypergraph_FO0402 | 61 | 0.993 | i=0 | | |
| voloshin-hypergraph_FO0403 | 61 | 0.992 | i+1 | | |
| voloshin-hypergraph_FO0404 | 62 | 1.000 | i:=i+1 | | |
| voloshin-hypergraph_FO0405 | 62 | 1.000 | N(S) | | |
| voloshin-hypergraph_FO0406 | 62 | 1.000 | G=(X, Y ; E) | | |
| voloshin-hypergraph_FO0407 | 62 | 1.000 | N_{G}(S) | | |
| voloshin-hypergraph_FO0408 | 63 | 1.000 | |S| | | |
| voloshin-hypergraph_FO0409 | 63 | 1.000 | \left|N_{G}(S)\right| \geq|S| | | |
| voloshin-hypergraph_FO0410 | 63 | 1.000 | |X| | | |
| voloshin-hypergraph_FO0411 | 63 | 1.000 | |X|=1 | | |
| voloshin-hypergraph_FO0412 | 63 | 1.000 | |X|>1 | | |
| voloshin-hypergraph_FO0413 | 63 | 1.000 | <|X| | | |
| voloshin-hypergraph_FO0414 | 63 | 1.000 | S \subset X, S \neq X | | |
| voloshin-hypergraph_FO0415 | 63 | 1.000 | G^{\prime}=\left(X^{\prime}, Y^{\prime} ; E^{\prime}\right) | | |
| voloshin-hypergraph_FO0416 | 63 | 1.000 | \left|X^{\prime}\right|=|X|-1<|X| | | |
| voloshin-hypergraph_FO0417 | 63 | 1.000 | S^{\prime} \subseteq X^{\prime} | | |
| voloshin-hypergraph_FO0418 | 63 | 1.000 | S_{0} \subset X, S_{0} \neq X | | |
| voloshin-hypergraph_FO0419 | 63 | 1.000 | G_{A} | | |
| voloshin-hypergraph_FO0420 | 63 | 1.000 | G_{B} | | |
| voloshin-hypergraph_FO0421 | 63 | 1.000 | S \subseteq S_{0} | | |
| voloshin-hypergraph_FO0422 | 63 | 1.000 | N_{G_{A}}(S)=N_{G}(S) | | |
| voloshin-hypergraph_FO0423 | 63 | 1.000 | |S| \leq\left|N_{G_{A}}(S)\right| | | |
| voloshin-hypergraph_FO0424 | 63 | 1.000 | S_{0} | | |
| voloshin-hypergraph_FO0425 | 63 | 1.000 | S \subseteq X-S_{0} | | |
| voloshin-hypergraph_FO0426 | 64 | 1.000 | \left|S_{0}\right|=\left|N_{G}\left(S_{0}\right)\right| | | |
| voloshin-hypergraph_FO0427 | 64 | 1.000 | |S| \leq\left|N_{G_{B}}(S)\right| | | |
| voloshin-hypergraph_FO0428 | 64 | 1.000 | X-S_{0} | | |
| voloshin-hypergraph_FO0429 | 64 | 0.746 | k \geq 1 | | |
| voloshin-hypergraph_FO0430 | 64 | 1.000 | k|X|=k|Y| | | |
| voloshin-hypergraph_FO0431 | 64 | 1.000 | |X|=|Y| | | |
| voloshin-hypergraph_FO0432 | 64 | 1.000 | i=k|S| | | |
| voloshin-hypergraph_FO0433 | 64 | 1.000 | k, i \leq k\left|N_{G}(S)\right| | | |
| voloshin-hypergraph_FO0434 | 64 | 1.000 | S \subseteq X,\left|N_{G}(S)\right| \geq|S| | | |
| voloshin-hypergraph_FO0435 | 64 | 0.987 | G, \tau(G) \geq v(G) | | |
| voloshin-hypergraph_FO0436 | 65 | 1.000 | T \subseteq(X \cup Y) | | |
| voloshin-hypergraph_FO0437 | 65 | 1.000 | \tau(G)=|T| | | |
| voloshin-hypergraph_FO0438 | 65 | 0.999 | X \cap T=A | | |
| voloshin-hypergraph_FO0439 | 65 | 0.999 | Y \cap T=B | | |
| voloshin-hypergraph_FO0440 | 65 | 0.999 | G_{1}=G_{A \cup(Y \backslash B)} | | |
| voloshin-hypergraph_FO0441 | 65 | 0.999 | G_{2}=G_{B \cup(X \backslash A)} | | |
| voloshin-hypergraph_FO0442 | 65 | 1.000 | A \cup B | | |
| voloshin-hypergraph_FO0443 | 65 | 1.000 | Y \backslash B | | |
| voloshin-hypergraph_FO0444 | 65 | 1.000 | X \backslash A | | |
| voloshin-hypergraph_FO0445 | 65 | 1.000 | S \subseteq A | | |
| voloshin-hypergraph_FO0446 | 65 | 1.000 | N_{G_{1}}(S) | | |
| voloshin-hypergraph_FO0447 | 65 | 1.000 | \left|N_{G_{1}}(S)\right|<|S| | | |
| voloshin-hypergraph_FO0448 | 65 | 1.000 | \left|N_{G_{1}}(S)\right| \geq|S| | | |
| voloshin-hypergraph_FO0449 | 65 | 0.887 | |A|+|B|=|T|=\tau(G) | | |
| voloshin-hypergraph_FO0450 | 65 | 0.887 | \tau(G)=v(G) | | |
| voloshin-hypergraph_FO0451 | 65 | 1.000 | m, n \geq 1 | | |
| voloshin-hypergraph_FO0452 | 65 | 1.000 | K_{m, n} | | |
| voloshin-hypergraph_FO0453 | 65 | 0.999 | \tau\left(K_{m, n}\right) | | |
| voloshin-hypergraph_FO0454 | 65 | 0.999 | v\left(K_{m, n}\right) | | |
| voloshin-hypergraph_FO0455 | 65 | 0.637 | \tau | | |
| voloshin-hypergraph_FO0456 | 67 | 1.000 | \geq 4 | | |
| voloshin-hypergraph_FO0457 | 67 | 1.000 | C_{1}, C_{2} | | |
| voloshin-hypergraph_FO0458 | 68 | 1.000 | G_{1}=G_{X_{1} \cup S} | | |
| voloshin-hypergraph_FO0459 | 68 | 1.000 | G_{2}=G_{X_{2} \cup S} | | |
| voloshin-hypergraph_FO0460 | 68 | 1.000 | G_{S} | | |
| voloshin-hypergraph_FO0461 | 68 | 1.000 | x, y \in S | | |
| voloshin-hypergraph_FO0462 | 69 | 0.997 | y . C_{k} | | |
| voloshin-hypergraph_FO0463 | 69 | 1.000 | k \geq 4 | | |
| voloshin-hypergraph_FO0464 | 69 | 1.000 | |X|= | | |
| voloshin-hypergraph_FO0465 | 69 | 1.000 | X-\{x, y\} | | |
| voloshin-hypergraph_FO0466 | 69 | 1.000 | G_{X_{1}} | | |
| voloshin-hypergraph_FO0467 | 69 | 1.000 | G_{X_{2}} | | |
| voloshin-hypergraph_FO0468 | 69 | 1.000 | <n | | |
| voloshin-hypergraph_FO0469 | 69 | 0.549 | X_{2} \neq \emptyset | | |
| voloshin-hypergraph_FO0470 | 69 | 1.000 | K_{n}, n \geq 2 | | |
| voloshin-hypergraph_FO0471 | 70 | 1.000 | G_{1}=(X, E) | | |
| voloshin-hypergraph_FO0472 | 70 | 0.875 | G_{n+1}=\emptyset | | |
| voloshin-hypergraph_FO0473 | 70 | 0.999 | \boldsymbol{\sigma}=\left(x_{1}, x_{2}, \ldots, x_{n}\right) | | |
| voloshin-hypergraph_FO0474 | 70 | 1.000 | x_{i}, x_{i+1}, \ldots, x_{n} | | |
| voloshin-hypergraph_FO0475 | 70 | 1.000 | G_{i+1}=G_{i}-x_{i}, i=1,2, \ldots, n | | |
| voloshin-hypergraph_FO0478 | 70 | 0.846 | \boldsymbol{\sigma}=(1,2,3,4,5,6,7,8) | | |
| voloshin-hypergraph_FO0479 | 70 | 0.907 | \binom{8}{4} | | |
| voloshin-hypergraph_FO0480 | 70 | 0.943 | \binom{8}{5} | | |
| voloshin-hypergraph_FO0481 | 70 | 0.668 | \binom{8}{6} | | |
| voloshin-hypergraph_FO0482 | 70 | 0.668 | C_{6},\binom{8}{7} | | |
| voloshin-hypergraph_FO0483 | 70 | 0.668 | C_{8} | | |
| voloshin-hypergraph_FO0484 | 70 | 0.668 | \binom{8}{8} | | |
| voloshin-hypergraph_FO0485 | 71 | 1.000 | \sigma^{\prime}=(2,3,8,7,6,5,4,1) | | |
| voloshin-hypergraph_FO0486 | 71 | 1.000 | S^{\prime} | | |
| voloshin-hypergraph_FO0487 | 71 | 1.000 | \{x\} \cup N(x) | | |
| voloshin-hypergraph_FO0488 | 71 | 1.000 | S^{\prime} \cup\{x\} | | |
| voloshin-hypergraph_FO0489 | 71 | 1.000 | y \in N(x) | | |
| voloshin-hypergraph_FO0490 | 71 | 1.000 | y \in S^{\prime} | | |
| voloshin-hypergraph_FO0491 | 71 | 1.000 | S=S^{\prime} \backslash\{y\} \cup\{x\} | | |
| voloshin-hypergraph_FO0492 | 71 | 0.995 | |S|=\alpha(G) | | |
| voloshin-hypergraph_FO0493 | 71 | 0.872 | S=\emptyset | | |
| voloshin-hypergraph_FO0494 | 72 | 0.813 | \{1,4,5\} | | |
| voloshin-hypergraph_FO0495 | 72 | 1.000 | \{2,3,8\} | | |
| voloshin-hypergraph_FO0496 | 72 | 0.968 | S=\{1,2,6\} | | |
| voloshin-hypergraph_FO0497 | 72 | 0.968 | \alpha(G)=3 | | |
| voloshin-hypergraph_FO0498 | 72 | 1.000 | \{3,4,5,7,8\} | | |
| voloshin-hypergraph_FO0499 | 72 | 1.000 | \tau(G)=5 | | |
| voloshin-hypergraph_FO0500 | 72 | 0.966 | \{1,4,5\},\{2,3,8\} | | |
| voloshin-hypergraph_FO0501 | 72 | 0.999 | \theta(G) | | |
| voloshin-hypergraph_FO0502 | 72 | 0.986 | \theta(G)=3 | | |
| voloshin-hypergraph_FO0503 | 73 | 1.000 | M(G) | | |
| voloshin-hypergraph_FO0504 | 73 | 1.000 | t | | |
| voloshin-hypergraph_FO0505 | 73 | 1.000 | M(G)>t | | |
| voloshin-hypergraph_FO0507 | 73 | 1.000 | G, M(G) \geq \omega(G)-1 | | |
| voloshin-hypergraph_FO0508 | 73 | 0.999 | \omega(G)-1 | | |
| voloshin-hypergraph_FO0509 | 74 | 0.969 | \boldsymbol{\omega}(G)-1 | | |
| voloshin-hypergraph_FO0510 | 74 | 1.000 | M\left(G^{\prime}\right)=\omega\left(G^{\prime}\right)-1 | | |
| voloshin-hypergraph_FO0511 | 74 | 1.000 | M\left(C_{k}\right)=2=\omega\left(C_{k}\right) | | |
| voloshin-hypergraph_FO0512 | 74 | 1.000 | M(G) \geq \omega(G)-1 | | |
| voloshin-hypergraph_FO0513 | 74 | 1.000 | \omega(G)=t+1 | | |
| voloshin-hypergraph_FO0514 | 74 | 1.000 | M(G) \leq t=\omega(G)-1 | | |
| voloshin-hypergraph_FO0515 | 74 | 1.000 | M(G)=\omega(G)-1 | | |
| voloshin-hypergraph_FO0516 | 74 | 1.000 | K_{n, n} | | |
| voloshin-hypergraph_FO0517 | 74 | 1.000 | M\left(K_{n, n}\right)=n, \omega\left(K_{n, n}\right)=2 | | |
| voloshin-hypergraph_FO0518 | 74 | 1.000 | M\left(G^{\prime}\right)>\omega\left(G^{\prime}\right)-1 | | |
| voloshin-hypergraph_FO0519 | 74 | 1.000 | M\left(C_{n}\right), M\left(K_{n}\right), M\left(W_{n}\right) | | |
| voloshin-hypergraph_FO0520 | 74 | 1.000 | G, M(G)=k | | |
| voloshin-hypergraph_FO0521 | 75 | 1.000 | G= | | |
| voloshin-hypergraph_FO0522 | 75 | 0.998 | (X, E) | | |
| voloshin-hypergraph_FO0523 | 75 | 0.998 | n=2 | | |
| voloshin-hypergraph_FO0524 | 75 | 0.999 | N_{k}=N_{\infty}(x) | | |
| voloshin-hypergraph_FO0525 | 76 | 1.000 | N_{\infty}(x)=X-\{x\} | | |
| voloshin-hypergraph_FO0526 | 76 | 1.000 | G-x | | |
| voloshin-hypergraph_FO0527 | 76 | 1.000 | N_{k-1} | | |
| voloshin-hypergraph_FO0528 | 76 | 1.000 | G_{N_{k}} | | |
| voloshin-hypergraph_FO0529 | 76 | 1.000 | G_{N_{k-1}} | | |
| voloshin-hypergraph_FO0530 | 76 | 1.000 | G_{N_{k-1} \cup N_{k}} | | |
| voloshin-hypergraph_FO0531 | 76 | 1.000 | y \in N_{k} | | |
| voloshin-hypergraph_FO0532 | 76 | 0.976 | y^{\prime} \in N_{\infty}(x) | | |
| voloshin-hypergraph_FO0533 | 76 | 0.986 | d\left(x, y^{\prime}\right)=d(x, y)=\operatorname{diam}(G) | | |
| voloshin-hypergraph_FO0534 | 76 | 0.934 | y^{\prime} | | |
| voloshin-hypergraph_FO0535 | 76 | 0.934 | x^{\prime} \in N_{\infty}\left(y^{\prime}\right) | | |
| voloshin-hypergraph_FO0536 | 76 | 0.934 | d\left(y^{\prime}, x^{\prime}\right)=d\left(y^{\prime}, x\right)=\operatorname{diam}(G) | | |
| voloshin-hypergraph_FO0537 | 76 | 0.997 | \operatorname{diam}(G)=4 | | |
| voloshin-hypergraph_FO0538 | 76 | 0.997 | N_{0}=\{2\} | | |
| voloshin-hypergraph_FO0539 | 76 | 0.997 | N_{1}(2)=\{1,12,10,3\} | | |
| voloshin-hypergraph_FO0540 | 76 | 1.000 | N_{2}(2)=\{11,4,8,9\} | | |
| voloshin-hypergraph_FO0541 | 76 | 1.000 | N_{3}(2)=N_{\infty}(2)=\{5,6,7\} | | |
| voloshin-hypergraph_FO0542 | 77 | 0.997 | N_{0}(5)=\{5\}, N_{1}(5)=\{4,6\} | | |
| voloshin-hypergraph_FO0543 | 77 | 1.000 | N_{2}(5)=\{7,8,9,3\}, N_{3}(5)=\{2,10\}, N_{4}(5)=N_{\infty}(5)=\{1,12,11\} | | |
| voloshin-hypergraph_FO0544 | 77 | 0.993 | d(11,5)=\operatorname{diam}(G)=4 | | |
| voloshin-hypergraph_FO0545 | 78 | 1.000 | \overline{C_{l}}, l \geq 4 | | |
| voloshin-hypergraph_FO0546 | 78 | 1.000 | C_{k}, k \geq 6 | | |
| voloshin-hypergraph_FO0547 | 78 | 1.000 | \overline{C_{4}} | | |
| voloshin-hypergraph_FO0548 | 79 | 0.971 | G-S | | |
| voloshin-hypergraph_FO0549 | 79 | 1.000 | y, z \in S | | |
| voloshin-hypergraph_FO0550 | 80 | 1.000 | n(G) | | |
| voloshin-hypergraph_FO0551 | 80 | 1.000 | C_{l}, l \geq 4 | | |
| voloshin-hypergraph_FO0552 | 80 | 0.989 | X^{\prime} \neq \emptyset | | |
| voloshin-hypergraph_FO0553 | 80 | 1.000 | G^{\prime}=G-X^{\prime} | | |
| voloshin-hypergraph_FO0554 | 80 | 1.000 | X^{\prime}=X | | |
| voloshin-hypergraph_FO0555 | 80 | 1.000 | n\left(G^{\prime}\right)<n(G) | | |
| voloshin-hypergraph_FO0556 | 80 | 1.000 | C_{k}, k \geq 4, y | | |
| voloshin-hypergraph_FO0557 | 80 | 1.000 | G=G_{1} \cup G_{2}, G_{1} \cap G_{2}=S | | |
| voloshin-hypergraph_FO0558 | 80 | 1.000 | G_{1}-S | | |
| voloshin-hypergraph_FO0559 | 80 | 1.000 | G_{2}-S | | |
| voloshin-hypergraph_FO0560 | 80 | 1.000 | e_{1}, e_{2} | | |
| voloshin-hypergraph_FO0561 | 81 | 1.000 | S \subseteq N(x) | | |
| voloshin-hypergraph_FO0562 | 81 | 1.000 | X^{\prime}, y | | |
| voloshin-hypergraph_FO0563 | 82 | 1.000 | C_{n}, K_{n}, W_{n}, n \geq 3 | | |
| voloshin-hypergraph_FO0564 | 83 | 1.000 | f(G) | | |
| voloshin-hypergraph_FO0565 | 83 | 1.000 | f_{1} | | |
| voloshin-hypergraph_FO0566 | 83 | 1.000 | f_{4} | | |
| voloshin-hypergraph_FO0567 | 85 | 1.000 | K_{2,3} | | |
| voloshin-hypergraph_FO0568 | 85 | 1.000 | W_{n}(n \geq 4) | | |
| voloshin-hypergraph_FO0569 | 85 | 1.000 | m(T)=n-1, f(T)=1 | | |
| voloshin-hypergraph_FO0570 | 85 | 1.000 | n(T)- | | |
| voloshin-hypergraph_FO0571 | 85 | 1.000 | m(T)+f(T)=n-(n-1)+1=2 | | |
| voloshin-hypergraph_FO0572 | 85 | 1.000 | m-n+2 | | |
| voloshin-hypergraph_FO0573 | 85 | 1.000 | m(G) | | |
| voloshin-hypergraph_FO0574 | 85 | 1.000 | f(G)= | | |
| voloshin-hypergraph_FO0575 | 85 | 1.000 | 3 f | | |
| voloshin-hypergraph_FO0576 | 85 | 1.000 | 2 m | | |
| voloshin-hypergraph_FO0577 | 85 | 1.000 | 3 f \leq 2 m | | |
| voloshin-hypergraph_FO0578 | 85 | 1.000 | f=2-n+m | | |
| voloshin-hypergraph_FO0579 | 85 | 1.000 | 3(2-n+m) \leq 2 m | | |
| voloshin-hypergraph_FO0580 | 85 | 1.000 | m \leq 3 n-6 | | |
| voloshin-hypergraph_FO0581 | 86 | 0.615 | 6 n \leq 2 m | | |
| voloshin-hypergraph_FO0582 | 86 | 1.000 | 3 n \leq m | | |
| voloshin-hypergraph_FO0583 | 86 | 1.000 | 3 n \leq m \leq 3 n-6 | | |
| voloshin-hypergraph_FO0584 | 86 | 1.000 | 0 \leq-6 | | |
| voloshin-hypergraph_FO0585 | 86 | 0.997 | n-m+ | | |
| voloshin-hypergraph_FO0586 | 86 | 1.000 | f=2 | | |
| voloshin-hypergraph_FO0587 | 87 | 1.000 | n=8, m=12, f=6 | | |
| voloshin-hypergraph_FO0588 | 87 | 1.000 | K_{n}, W_{n}, K_{m, n}(m \geq 1, n \geq 3) | | |
| voloshin-hypergraph_FO0589 | 89 | 1.000 | X=\{1,2,3,4,5,6\} | | |
| voloshin-hypergraph_FO0590 | 90 | 1.000 | k, l \geq 3 | | |
| voloshin-hypergraph_FO0591 | 90 | 0.995 | G_{i}^{\prime}=G_{i} \cup\{x, y\} | | |
| voloshin-hypergraph_FO0592 | 90 | 1.000 | G_{1}^{\prime}, G_{2}^{\prime} | | |
| voloshin-hypergraph_FO0593 | 90 | 1.000 | \geq 5 | | |
| voloshin-hypergraph_FO0594 | 91 | 1.000 | G-V\left(G^{\prime}\right) | | |
| voloshin-hypergraph_FO0595 | 91 | 1.000 | F(A) | | |
| voloshin-hypergraph_FO0596 | 91 | 1.000 | F(A)=\emptyset | | |
| voloshin-hypergraph_FO0597 | 91 | 1.000 | |F(A)|=1 | | |
| voloshin-hypergraph_FO0598 | 91 | 1.000 | |F(A)|>1 | | |
| voloshin-hypergraph_FO0599 | 91 | 1.000 | G^{\prime} \neq G | | |
| voloshin-hypergraph_FO0600 | 91 | 1.000 | m \geq 1 | | |
| voloshin-hypergraph_FO0601 | 91 | 1.000 | n \geq 3 | | |
| voloshin-hypergraph_FO0602 | 91 | 1.000 | K_{n}, K_{m, n}, W_{n} | | |
| voloshin-hypergraph_FO0603 | 92 | 1.000 | n \geq 4 | | |
| voloshin-hypergraph_FO0604 | 92 | 1.000 | m=3 n-6 | | |
| voloshin-hypergraph_FO0605 | 92 | 1.000 | 3 f=2 m | | |
| voloshin-hypergraph_FO0606 | 93 | 1.000 | m=3 n-6=15-6=9 | | |
| voloshin-hypergraph_FO0607 | 93 | 1.000 | G^{*} | | |
| voloshin-hypergraph_FO0608 | 93 | 1.000 | f_{i} | | |
| voloshin-hypergraph_FO0609 | 93 | 1.000 | f_{j} | | |
| voloshin-hypergraph_FO0610 | 93 | 1.000 | n\left(G^{*}\right)=f, m\left(G^{*}\right)=m | | |
| voloshin-hypergraph_FO0611 | 93 | 1.000 | f\left(G^{*}\right)=n | | |
| voloshin-hypergraph_FO0612 | 93 | 0.992 | \left(G^{*}\right)^{*} | | |
| voloshin-hypergraph_FO0613 | 94 | 1.000 | W_{n}, n \geq 4 | | |
| voloshin-hypergraph_FO0614 | 96 | 0.989 | 1,2, \ldots, \lambda | | |
| voloshin-hypergraph_FO0615 | 96 | 0.989 | \lambda | | |
| voloshin-hypergraph_FO0616 | 96 | 1.000 | \{1,2, \ldots, \lambda\} | | |
| voloshin-hypergraph_FO0617 | 96 | 1.000 | P(G, \lambda) | | |
| voloshin-hypergraph_FO0618 | 96 | 1.000 | \chi(G) | | |
| voloshin-hypergraph_FO0619 | 96 | 1.000 | \min \{n(G), \lambda\} | | |
| voloshin-hypergraph_FO0620 | 96 | 1.000 | P(G, \lambda)=0 | | |
| voloshin-hypergraph_FO0621 | 96 | 1.000 | 1 \leq \lambda \leq \chi(G)-1 | | |
| voloshin-hypergraph_FO0622 | 96 | 1.000 | \lambda \geq \chi(G) | | |
| voloshin-hypergraph_FO0623 | 96 | 1.000 | P(G, \lambda) \geq 1 | | |
| voloshin-hypergraph_FO0624 | 96 | 1.000 | X=\{x, y, z\} | | |
| voloshin-hypergraph_FO0625 | 96 | 1.000 | E=\{\{x, y\} | | |
| voloshin-hypergraph_FO0626 | 96 | 0.997 | \{y, z\}\} | | |
| voloshin-hypergraph_FO0627 | 96 | 0.997 | \chi(G)>1 | | |
| voloshin-hypergraph_FO0628 | 96 | 0.998 | \chi(G)=2 | | |
| voloshin-hypergraph_FO0629 | 96 | 0.998 | \{1,2,3\} | | |
| voloshin-hypergraph_FO0630 | 96 | 0.998 | \lambda=3 | | |
| voloshin-hypergraph_FO0631 | 96 | 1.000 | i=2 | | |
| voloshin-hypergraph_FO0632 | 96 | 1.000 | i=3 | | |
| voloshin-hypergraph_FO0633 | 96 | 0.523 | \binom{\lambda}{i}=\binom{3}{2}=3 | | |
| voloshin-hypergraph_FO0636 | 97 | 1.000 | r_{i}(G) | | |
| voloshin-hypergraph_FO0637 | 98 | 0.927 | X: X_{1}=\{x, z\} | | |
| voloshin-hypergraph_FO0638 | 98 | 0.927 | X_{2}=\{y\} | | |
| voloshin-hypergraph_FO0639 | 98 | 1.000 | r_{2}(G)=1 | | |
| voloshin-hypergraph_FO0640 | 98 | 1.000 | X_{1}=\{x\}, X_{2}=\{y\} | | |
| voloshin-hypergraph_FO0641 | 98 | 1.000 | X_{3}=\{z\} | | |
| voloshin-hypergraph_FO0642 | 98 | 1.000 | r_{3}(G)=1 | | |
| voloshin-hypergraph_FO0643 | 98 | 1.000 | r_{1}(G)=0 | | |
| voloshin-hypergraph_FO0644 | 98 | 1.000 | R(G) | | |
| voloshin-hypergraph_FO0645 | 98 | 0.850 | R(G)=\left(0,0, \ldots, 0, r_{\chi}, r_{\chi+1}, \ldots, r_{n}\right) | | |
| voloshin-hypergraph_FO0646 | 98 | 0.850 | r_{\chi}>0 | | |
| voloshin-hypergraph_FO0647 | 98 | 0.476 | \chi | | |
| voloshin-hypergraph_FO0648 | 98 | 0.987 | \chi+1 | | |
| voloshin-hypergraph_FO0649 | 98 | 0.360 | r_{\chi+1}>0 | | |
| voloshin-hypergraph_FO0650 | 98 | 1.000 | r_{\chi+2}>0, r_{\chi+3}>0, \ldots | | |
| voloshin-hypergraph_FO0651 | 98 | 1.000 | r_{n}=1>0 | | |
| voloshin-hypergraph_FO0652 | 98 | 1.000 | G, \chi(G) \leq 2 | | |
| voloshin-hypergraph_FO0653 | 98 | 1.000 | \chi(G) \leq \Delta(G) | | |
| voloshin-hypergraph_FO0654 | 98 | 1.000 | E_{n}, K_{n}, K_{m, n} | | |
| voloshin-hypergraph_FO0655 | 98 | 1.000 | T_{n}, C_{2 n}, C_{2 n+1}, W_{n} | | |
| voloshin-hypergraph_FO0656 | 98 | 1.000 | P\left(G^{\prime}, 3\right) | | |
| voloshin-hypergraph_FO0657 | 98 | 1.000 | R\left(G^{\prime}\right) | | |
| voloshin-hypergraph_FO0658 | 99 | 1.000 | i=6 | | |
| voloshin-hypergraph_FO0659 | 99 | 1.000 | i+1, i+2, \ldots, n=10 | | |
| voloshin-hypergraph_FO0660 | 99 | 0.904 | \chi, \chi+1, \chi+2, \ldots, n=10 | | |
| voloshin-hypergraph_FO0661 | 99 | 1.000 | \lambda \geq 1 | | |
| voloshin-hypergraph_FO0662 | 99 | 1.000 | \lambda<n | | |
| voloshin-hypergraph_FO0663 | 99 | 1.000 | \lambda \geq n | | |
| voloshin-hypergraph_FO0664 | 99 | 1.000 | \chi\left(K_{n}\right)=n | | |
| voloshin-hypergraph_FO0665 | 99 | 1.000 | P\left(K_{n}, \lambda\right) | | |
| voloshin-hypergraph_FO0666 | 99 | 0.647 | \lambda-1 | | |
| voloshin-hypergraph_FO0667 | 99 | 0.647 | \lambda-2 | | |
| voloshin-hypergraph_FO0670 | 100 | 1.000 | \lambda^{(n)} | | |
| voloshin-hypergraph_FO0673 | 100 | 1.000 | G \cdot e | | |
| voloshin-hypergraph_FO0677 | 101 | 1.000 | s \geq 1 | | |
| voloshin-hypergraph_FO0678 | 101 | 1.000 | P\left(K_{i_{j}}, \lambda\right) | | |
| voloshin-hypergraph_FO0679 | 101 | 1.000 | K_{i_{1}}, K_{i_{2}}, \ldots, K_{i_{s}} | | |
| voloshin-hypergraph_FO0680 | 101 | 1.000 | K_{i} | | |
| voloshin-hypergraph_FO0681 | 101 | 0.996 | x y z | | |
| voloshin-hypergraph_FO0682 | 102 | 0.998 | r_{1}=r_{2}=\cdots=r_{\chi-1}=0 | | |
| voloshin-hypergraph_FO0683 | 102 | 0.998 | P\left(K_{i}, \lambda\right)=\lambda^{(i)} | | |
| voloshin-hypergraph_FO0684 | 102 | 0.998 | \left(\lambda^{(i)}\right) | | |
| voloshin-hypergraph_FO0685 | 102 | 0.875 | \left(r_{i}(G) \lambda^{(i)}\right) | | |
| voloshin-hypergraph_FO0686 | 102 | 0.875 | \sum_{i=\mathrm{x}}^{n} r_{i}(G) \lambda^{(i)} | | |
| voloshin-hypergraph_FO0687 | 102 | 1.000 | P(G, 3)=3(3-1)^{2}=12 | | |
| voloshin-hypergraph_FO0688 | 102 | 1.000 | P(G, \lambda)=P\left(K_{3}, \lambda\right)+P\left(K_{2}, \lambda\right)=0 \cdot P\left(K_{1}, \lambda\right)+ | | |
| voloshin-hypergraph_FO0689 | 102 | 1.000 | 1 \cdot P\left(K_{2}, \lambda\right)+1 \cdot P\left(K_{3}, \lambda\right) | | |
| voloshin-hypergraph_FO0690 | 102 | 1.000 | R(G)=(0,1,1) | | |
| voloshin-hypergraph_FO0691 | 102 | 1.000 | G_{3}, G_{4}, G_{5} | | |
| voloshin-hypergraph_FO0692 | 102 | 1.000 | G_{6} | | |
| voloshin-hypergraph_FO0693 | 103 | 1.000 | K_{i_{j}} | | |
| voloshin-hypergraph_FO0694 | 103 | 1.000 | P\left(C_{4}, 10\right)=10 \cdot 9 \cdot\left(10^{2}-3 \cdot 10+3\right)=6570 | | |
| voloshin-hypergraph_FO0695 | 104 | 1.000 | E_{4}, E_{5}, C_{5}, C_{6}, W_{4}, W_{5}, P_{4}, P_{5}, P_{6} | | |
| voloshin-hypergraph_FO0696 | 104 | 1.000 | n \geq 6 | | |
| voloshin-hypergraph_FO0697 | 104 | 1.000 | P_{4}, P_{5}, P_{6}, C_{5} | | |
| voloshin-hypergraph_FO0698 | 105 | 1.000 | P\left(G_{1}, \lambda\right) | | |
| voloshin-hypergraph_FO0699 | 105 | 1.000 | P\left(G_{2}, \lambda\right) | | |
| voloshin-hypergraph_FO0700 | 105 | 1.000 | E_{n}=n K_{1} | | |
| voloshin-hypergraph_FO0701 | 105 | 1.000 | P\left(K_{1}, \lambda\right)=\lambda | | |
| voloshin-hypergraph_FO0702 | 105 | 1.000 | S(n, i)=r_{i}\left(E_{n}\right) | | |
| voloshin-hypergraph_FO0703 | 105 | 1.000 | S(n, i) | | |
| voloshin-hypergraph_FO0704 | 106 | 1.000 | R\left(E_{1}\right)=(1), R\left(E_{2}\right)=(1,1), R\left(E_{3}\right)=(1,3,1) | | |
| voloshin-hypergraph_FO0705 | 106 | 1.000 | R\left(E_{4}\right)=(1,7,6,1) | | |
| voloshin-hypergraph_FO0706 | 106 | 0.890 | \lambda^{(4)}=-6 \lambda+11 \lambda^{2}- | | |
| voloshin-hypergraph_FO0707 | 106 | 1.000 | 6 \lambda^{3}+\lambda^{4} | | |
| voloshin-hypergraph_FO0708 | 106 | 1.000 | s(4,1)=-6, s(4,2)=11, s(4,3)=-6 | | |
| voloshin-hypergraph_FO0709 | 106 | 1.000 | s(4,4)=1 | | |
| voloshin-hypergraph_FO0710 | 106 | 1.000 | \lambda^{n} | | |
| voloshin-hypergraph_FO0711 | 106 | 1.000 | \lambda^{(i)} | | |
| voloshin-hypergraph_FO0712 | 106 | 1.000 | \lambda^{i}, i=1,2, \ldots, n | | |
| voloshin-hypergraph_FO0713 | 106 | 0.736 | 1,-m(G), \ldots | | |
| voloshin-hypergraph_FO0714 | 106 | 0.998 | m=0 | | |
| voloshin-hypergraph_FO0715 | 106 | 1.000 | G=E_{n} | | |
| voloshin-hypergraph_FO0716 | 106 | 1.000 | P(G, \lambda)=\lambda^{n} | | |
| voloshin-hypergraph_FO0717 | 106 | 1.000 | m>1 | | |
| voloshin-hypergraph_FO0718 | 106 | 1.000 | \left\{a_{i}\right\} | | |
| voloshin-hypergraph_FO0719 | 106 | 1.000 | \left\{b_{i}\right\} | | |
| voloshin-hypergraph_FO0720 | 107 | 1.000 | \lambda^{(k)} | | |
| voloshin-hypergraph_FO0721 | 107 | 1.000 | P(G, \lambda) / \lambda^{(k)} | | |
| voloshin-hypergraph_FO0722 | 107 | 1.000 | N_{1}=N_{2} | | |
| voloshin-hypergraph_FO0723 | 107 | 1.000 | j | | |
| voloshin-hypergraph_FO0724 | 108 | 1.000 | t=P\left(G_{S}, \lambda\right)=P\left(K_{k}, \lambda\right)=\lambda^{(k)} | | |
| voloshin-hypergraph_FO0725 | 108 | 1.000 | N_{1}=N_{2}=N_{3}=\cdots=N_{t} | | |
| voloshin-hypergraph_FO0726 | 108 | 1.000 | k-1 | | |
| voloshin-hypergraph_FO0727 | 108 | 1.000 | P\left(G_{X_{1} \cup S}, \lambda\right) | | |
| voloshin-hypergraph_FO0728 | 108 | 1.000 | P\left(G_{S}, \lambda\right)=\lambda^{(k)} | | |
| voloshin-hypergraph_FO0729 | 108 | 1.000 | P\left(G_{X_{1} \cup S}, \lambda\right) / \lambda^{(k)} | | |
| voloshin-hypergraph_FO0730 | 108 | 1.000 | P\left(G_{X_{2} \cup S}, \lambda\right) | | |
| voloshin-hypergraph_FO0731 | 108 | 1.000 | P\left(G_{X_{2} \cup S}, \lambda\right) / \lambda^{(k)} | | |
| voloshin-hypergraph_FO0732 | 109 | 0.947 | G_{1}, G_{2}, \ldots G_{l} | | |
| voloshin-hypergraph_FO0733 | 109 | 0.996 | G_{i}, i=1,2, \ldots, l | | |
| voloshin-hypergraph_FO0734 | 109 | 0.733 | P(\emptyset, \lambda)=1 | | |
| voloshin-hypergraph_FO0735 | 109 | 1.000 | G_{1}=C_{4}, G_{2}=K_{3} | | |
| voloshin-hypergraph_FO0736 | 109 | 1.000 | |S|=2 | | |
| voloshin-hypergraph_FO0737 | 109 | 1.000 | P\left(C_{4}, \lambda\right) | | |
| voloshin-hypergraph_FO0738 | 109 | 1.000 | P\left(K_{3}, \lambda\right)=\lambda(\lambda-1)(\lambda-2) | | |
| voloshin-hypergraph_FO0739 | 109 | 0.986 | X_{2}=\{x\} | | |
| voloshin-hypergraph_FO0742 | 110 | 1.000 | G=K_{k+1}, G-x=K_{k} | | |
| voloshin-hypergraph_FO0743 | 110 | 1.000 | G_{1}=G-x=C_{4} | | |
| voloshin-hypergraph_FO0744 | 110 | 0.999 | (i-k) r_{i}(G-x) | | |
| voloshin-hypergraph_FO0745 | 110 | 1.000 | r_{i-1}(G-x) | | |
| voloshin-hypergraph_FO0746 | 110 | 1.000 | E_{n}: r_{i}\left(E_{n}\right)=S(n, i) | | |
| voloshin-hypergraph_FO0747 | 110 | 1.000 | r_{1}\left(E_{1}\right)=S(1,1)=1 | | |
| voloshin-hypergraph_FO0748 | 110 | 1.000 | P_{3}, P_{4}, P_{5}, P_{n} | | |
| voloshin-hypergraph_FO0749 | 110 | 1.000 | C_{4}, C_{5}, C_{6}, C_{7} | | |
| voloshin-hypergraph_FO0750 | 110 | 1.000 | W_{4}, W_{5}, W_{6} | | |
| voloshin-hypergraph_FO0751 | 111 | 1.000 | E_{6}, E_{7} | | |
| voloshin-hypergraph_FO0752 | 111 | 1.000 | E_{8} | | |
| voloshin-hypergraph_FO0753 | 111 | 1.000 | K_{3}, K_{4}, K_{5} | | |
| voloshin-hypergraph_FO0754 | 111 | 1.000 | i \leq n | | |
| voloshin-hypergraph_FO0755 | 111 | 0.994 | G_{1}=(X, E),|X|=n | | |
| voloshin-hypergraph_FO0756 | 111 | 0.999 | G_{2}=G_{1}-x_{1}, G_{3}=G_{2}-x_{2}, \ldots, G_{n}=G_{n-1}-x_{n-1}=\left\{x_{n}\right\} | | |
| voloshin-hypergraph_FO0757 | 111 | 0.858 | G_{n+1}=G_{n}-x_{n}=\emptyset | | |
| voloshin-hypergraph_FO0758 | 111 | 0.858 | k_{i} | | |
| voloshin-hypergraph_FO0759 | 111 | 1.000 | G_{i}, i=1, \ldots, n | | |
| voloshin-hypergraph_FO0760 | 111 | 1.000 | G_{n} | | |
| voloshin-hypergraph_FO0761 | 111 | 1.000 | k_{n}=0 | | |
| voloshin-hypergraph_FO0762 | 111 | 1.000 | \lambda=0 | | |
| voloshin-hypergraph_FO0763 | 112 | 1.000 | \omega\left(G_{1}\right) | | |
| voloshin-hypergraph_FO0764 | 112 | 1.000 | \omega\left(G_{1}\right)-1 | | |
| voloshin-hypergraph_FO0765 | 112 | 1.000 | \lambda=\omega\left(G_{1}\right)-1 | | |
| voloshin-hypergraph_FO0766 | 112 | 1.000 | \omega\left(G_{1}\right) \leq \chi\left(G_{1}\right) | | |
| voloshin-hypergraph_FO0767 | 112 | 0.999 | \omega | | |
| voloshin-hypergraph_FO0768 | 112 | 0.987 | [0, \omega-1] | | |
| voloshin-hypergraph_FO0769 | 112 | 1.000 | \chi\left(G_{1}\right)=\omega\left(G_{1}\right) | | |
| voloshin-hypergraph_FO0770 | 112 | 0.866 | x_{n}, x_{n-1}, x_{n-2}, \ldots, x_{2}, x_{1} | | |
| voloshin-hypergraph_FO0771 | 112 | 0.993 | x_{n-1} | | |
| voloshin-hypergraph_FO0772 | 112 | 0.699 | x_{n-2} | | |
| voloshin-hypergraph_FO0773 | 112 | 0.982 | \omega-1 | | |
| voloshin-hypergraph_FO0774 | 112 | 1.000 | \omega(G)=\chi(G) | | |
| voloshin-hypergraph_FO0775 | 112 | 0.995 | s_{i} \geq 1(i=0,1, \ldots, \chi-1) | | |
| voloshin-hypergraph_FO0776 | 112 | 0.531 | 2,2,1,0 | | |
| voloshin-hypergraph_FO0777 | 113 | 1.000 | \omega\left(G_{1}\right)=\chi\left(G_{1}\right)=4 | | |
| voloshin-hypergraph_FO0778 | 113 | 1.000 | k_{1}=k_{2}=\cdots=k_{n-1}=1, k_{n}=0 | | |
| voloshin-hypergraph_FO0779 | 113 | 1.000 | C_{n}, n \geq 1 | | |
| voloshin-hypergraph_FO0780 | 113 | 1.000 | n=1,2,3 | | |
| voloshin-hypergraph_FO0781 | 114 | 0.987 | \chi^{\prime}=\chi\left(G^{\prime}\right) | | |
| voloshin-hypergraph_FO0782 | 114 | 0.987 | s_{i}^{\prime} \geq 1\left(i=0,1, \ldots, \chi^{\prime}-1\right) | | |
| voloshin-hypergraph_FO0783 | 114 | 1.000 | \chi\left(C_{k}\right)=2 | | |
| voloshin-hypergraph_FO0784 | 114 | 1.000 | \chi\left(C_{k}\right)=3 | | |
| voloshin-hypergraph_FO0785 | 114 | 1.000 | P\left(C_{k}, \lambda\right) | | |
| voloshin-hypergraph_FO0786 | 114 | 1.000 | \{0,1,2\} | | |
| voloshin-hypergraph_FO0787 | 114 | 1.000 | P\left(C_{k}, \lambda\right)=(\lambda-1)^{k}+ | | |
| voloshin-hypergraph_FO0788 | 114 | 1.000 | (-1)^{k}(\lambda-1) | | |
| voloshin-hypergraph_FO0789 | 114 | 0.997 | A \subset X | | |
| voloshin-hypergraph_FO0790 | 114 | 0.997 | G_{1}^{*}=\left(X_{1}, E_{1}\right), G_{2}^{*}= | | |
| voloshin-hypergraph_FO0791 | 114 | 1.000 | \left(X_{2}, E_{2}\right), \ldots, G_{k}^{*}=\left(X_{k}, E_{k}\right), k \geq 2 | | |
| voloshin-hypergraph_FO0792 | 114 | 1.000 | k>l | | |
| voloshin-hypergraph_FO0793 | 114 | 1.000 | X_{1} \cup X_{2} \cup \ldots \cup X_{k} \cup A=X | | |
| voloshin-hypergraph_FO0794 | 114 | 0.753 | X_{i} \cap X_{j}=\emptyset, i \neq j | | |
| voloshin-hypergraph_FO0795 | 114 | 1.000 | A^{\prime} \subset X^{\prime} | | |
| voloshin-hypergraph_FO0796 | 114 | 1.000 | G^{\prime}=G | | |
| voloshin-hypergraph_FO0797 | 114 | 1.000 | n=2,3,4 | | |
| voloshin-hypergraph_FO0798 | 114 | 1.000 | n>4 | | |
| voloshin-hypergraph_FO0799 | 114 | 1.000 | n(G)=n | | |
| voloshin-hypergraph_FO0800 | 114 | 1.000 | x_{0} \in X | | |
| voloshin-hypergraph_FO0801 | 114 | 1.000 | p | | |
| voloshin-hypergraph_FO0802 | 114 | 1.000 | x_{0} \notin A | | |
| voloshin-hypergraph_FO0803 | 114 | 1.000 | x_{0} \in X_{1} | | |
| voloshin-hypergraph_FO0804 | 114 | 1.000 | x_{0} | | |
| voloshin-hypergraph_FO0805 | 114 | 1.000 | N\left(x_{0}\right) \subseteq X_{1} \cup A | | |
| voloshin-hypergraph_FO0806 | 114 | 1.000 | G-x_{0} | | |
| voloshin-hypergraph_FO0807 | 114 | 1.000 | n\left(G-x_{0}\right)<n | | |
| voloshin-hypergraph_FO0808 | 115 | 0.958 | \lambda-p | | |
| voloshin-hypergraph_FO0809 | 115 | 1.000 | x_{0} \in A | | |
| voloshin-hypergraph_FO0810 | 115 | 1.000 | \left|N\left(x_{0}\right) \cap A\right|=p_{1} | | |
| voloshin-hypergraph_FO0811 | 115 | 1.000 | N\left(x_{0}\right) | | |
| voloshin-hypergraph_FO0812 | 115 | 1.000 | p-p_{1}=p_{2} | | |
| voloshin-hypergraph_FO0813 | 115 | 1.000 | X_{i}, 1 \leq i \leq n | | |
| voloshin-hypergraph_FO0814 | 115 | 1.000 | G_{i}, i= | | |
| voloshin-hypergraph_FO0815 | 115 | 1.000 | 0,2,3, \ldots, k | | |
| voloshin-hypergraph_FO0816 | 115 | 1.000 | p_{1} | | |
| voloshin-hypergraph_FO0817 | 115 | 1.000 | A-x_{0} | | |
| voloshin-hypergraph_FO0818 | 115 | 1.000 | G_{i}^{\prime} | | |
| voloshin-hypergraph_FO0819 | 115 | 1.000 | x_{0}, i=0,1, \ldots, k | | |
| voloshin-hypergraph_FO0820 | 115 | 1.000 | i=0,2, \ldots, k | | |
| voloshin-hypergraph_FO0821 | 116 | 1.000 | G_{1}, \ldots, G_{k} | | |
| voloshin-hypergraph_FO0822 | 116 | 1.000 | A=\emptyset | | |
| voloshin-hypergraph_FO0823 | 116 | 0.999 | x \in X^{\prime} | | |
| voloshin-hypergraph_FO0824 | 116 | 0.982 | X=\{x\} \cup N(x) | | |
| voloshin-hypergraph_FO0825 | 116 | 1.000 | X \neq\{x\} \cup N(x) | | |
| voloshin-hypergraph_FO0826 | 116 | 1.000 | G_{N(x)} | | |
| voloshin-hypergraph_FO0827 | 117 | 1.000 | C | | |
| voloshin-hypergraph_FO0828 | 117 | 1.000 | C-x | | |
| voloshin-hypergraph_FO0829 | 117 | 1.000 | C_{N(x)}=E_{2} | | |
| voloshin-hypergraph_FO0830 | 117 | 0.996 | P(C-x, \lambda)=\lambda(\lambda-1)^{k-2}, W\left(C_{N(x)}, \lambda\right)=\lambda^{-1}(\lambda-1)^{2} | | |
| voloshin-hypergraph_FO0831 | 117 | 1.000 | N(x)=K_{k} | | |
| voloshin-hypergraph_FO0832 | 117 | 1.000 | W\left(G_{N(4)}, \lambda\right) | | |
| voloshin-hypergraph_FO0833 | 117 | 1.000 | N(4)=\{1,5,6\} | | |
| voloshin-hypergraph_FO0834 | 118 | 1.000 | \{5,6,7,8\} | | |
| voloshin-hypergraph_FO0835 | 118 | 0.975 | G, \chi(G) \leq M(G)+1 | | |
| voloshin-hypergraph_FO0836 | 118 | 1.000 | G_{1}=G, G_{2}, G_{3}, \ldots, G_{n} | | |
| voloshin-hypergraph_FO0837 | 118 | 1.000 | x_{n}, x_{n-1}, \ldots, x_{2}, x_{1} | | |
| voloshin-hypergraph_FO0838 | 118 | 0.988 | (M(G)+1) | | |
| voloshin-hypergraph_FO0839 | 118 | 1.000 | M(G)+1 | | |
| voloshin-hypergraph_FO0841 | 119 | 0.999 | \chi(G) \leq 6 | | |
| voloshin-hypergraph_FO0842 | 119 | 1.000 | M(G) \leq 5 | | |
| voloshin-hypergraph_FO0843 | 119 | 1.000 | \chi(G) \leq 5 | | |
| voloshin-hypergraph_FO0844 | 119 | 1.000 | \leq 5 | | |
| voloshin-hypergraph_FO0845 | 119 | 0.998 | d(x) \leq 5 | | |
| voloshin-hypergraph_FO0846 | 119 | 0.998 | \chi(G-x) \leq 5 | | |
| voloshin-hypergraph_FO0847 | 119 | 0.693 | \leq 4 | | |
| voloshin-hypergraph_FO0848 | 119 | 0.988 | d(x)=5 | | |
| voloshin-hypergraph_FO0849 | 119 | 1.000 | G_{i}=G | | |
| voloshin-hypergraph_FO0850 | 119 | 0.999 | N(x)= | | |
| voloshin-hypergraph_FO0851 | 119 | 0.812 | (a, c) | | |
| voloshin-hypergraph_FO0852 | 119 | 0.812 | P | | |
| voloshin-hypergraph_FO0853 | 119 | 1.000 | a x | | |
| voloshin-hypergraph_FO0854 | 119 | 1.000 | x c | | |
| voloshin-hypergraph_FO0855 | 120 | 1.000 | G_{13} | | |
| voloshin-hypergraph_FO0856 | 120 | 0.725 | c | | |
| voloshin-hypergraph_FO0857 | 120 | 0.994 | \chi(G) \leq 4 | | |
| voloshin-hypergraph_FO0858 | 120 | 1.000 | \chi(G-x) \leq 4 | | |
| voloshin-hypergraph_FO0859 | 121 | 0.912 | \leq 3 | | |
| voloshin-hypergraph_FO0860 | 121 | 0.997 | d(x)=4 | | |
| voloshin-hypergraph_FO0861 | 121 | 0.999 | G^{\prime}=G-e | | |
| voloshin-hypergraph_FO0862 | 121 | 0.973 | N(x)=\{a, b, c, d, e\} | | |
| voloshin-hypergraph_FO0863 | 121 | 1.000 | a, b, c, d, e | | |
| voloshin-hypergraph_FO0864 | 121 | 1.000 | G_{i j} | | |
| voloshin-hypergraph_FO0865 | 121 | 1.000 | P_{i j} | | |
| voloshin-hypergraph_FO0866 | 121 | 0.936 | P_{13} | | |
| voloshin-hypergraph_FO0867 | 121 | 1.000 | (a, d) | | |
| voloshin-hypergraph_FO0868 | 121 | 1.000 | P_{14} | | |
| voloshin-hypergraph_FO0869 | 121 | 1.000 | G_{24} | | |
| voloshin-hypergraph_FO0870 | 121 | 1.000 | G^{\prime \prime} | | |
| voloshin-hypergraph_FO0871 | 121 | 1.000 | G_{23} | | |
| voloshin-hypergraph_FO0872 | 122 | 1.000 | x d | | |
| voloshin-hypergraph_FO0873 | 123 | 1.000 | \chi\left(W_{6}\right)=4 | | |
| voloshin-hypergraph_FO0874 | 124 | 1.000 | W_{8} | | |
| voloshin-hypergraph_FO0875 | 124 | 1.000 | P_{n}, K_{n}, K_{m, n}, C_{n}, W_{n}, m, n \geq 4 | | |
| voloshin-hypergraph_FO0876 | 124 | 1.000 | \chi(G)=4 | | |
| voloshin-hypergraph_FO0877 | 124 | 0.830 | \chi(G)=\omega(G) | | |
| voloshin-hypergraph_FO0878 | 124 | 0.830 | \chi(G)>\omega(G) | | |
| voloshin-hypergraph_FO0879 | 124 | 0.998 | \chi\left(C_{4}\right)=\omega\left(C_{4}\right)=2 | | |
| voloshin-hypergraph_FO0880 | 124 | 0.998 | \chi\left(C_{5}\right)=3>\omega\left(C_{5}\right)=2 | | |
| voloshin-hypergraph_FO0881 | 124 | 1.000 | \chi(G)-\omega(G) | | |
| voloshin-hypergraph_FO0882 | 125 | 0.997 | \chi=4 | | |
| voloshin-hypergraph_FO0883 | 125 | 1.000 | \omega=2 | | |
| voloshin-hypergraph_FO0884 | 125 | 0.970 | \boldsymbol{\chi}-\boldsymbol{\omega}=k | | |
| voloshin-hypergraph_FO0885 | 125 | 0.838 | \boldsymbol{\chi}-\boldsymbol{\omega} | | |
| voloshin-hypergraph_FO0886 | 125 | 0.838 | \boldsymbol{\omega}(G) | | |
| voloshin-hypergraph_FO0887 | 125 | 0.838 | \boldsymbol{\chi}(G) | | |
| voloshin-hypergraph_FO0888 | 126 | 1.000 | \chi\left(G^{\prime}\right)=\omega\left(G^{\prime}\right) | | |
| voloshin-hypergraph_FO0889 | 126 | 0.998 | \chi(G)=\theta(\bar{G}) | | |
| voloshin-hypergraph_FO0890 | 126 | 0.998 | \theta\left(G^{\prime}\right)=\alpha\left(G^{\prime}\right) | | |
| voloshin-hypergraph_FO0891 | 126 | 0.999 | \chi(G)=3, \omega(G)=3 | | |
| voloshin-hypergraph_FO0892 | 126 | 1.000 | \theta(G)=2 | | |
| voloshin-hypergraph_FO0893 | 126 | 1.000 | \chi(G)=2, \omega(G)=2, \alpha(G)=3 | | |
| voloshin-hypergraph_FO0894 | 126 | 1.000 | C_{5}: \chi\left(C_{5}\right)=3, \omega\left(C_{5}\right)=2, \alpha\left(C_{5}\right)=2 | | |
| voloshin-hypergraph_FO0895 | 126 | 0.972 | \theta\left(C_{5}\right)=3 | | |
| voloshin-hypergraph_FO0896 | 126 | 1.000 | \theta\left(G^{\prime}\right) \neq \alpha\left(G^{\prime}\right) | | |
| voloshin-hypergraph_FO0897 | 127 | 1.000 | n=3,4,5 | | |
| voloshin-hypergraph_FO0898 | 127 | 1.000 | \chi(G-x)= | | |
| voloshin-hypergraph_FO0899 | 127 | 1.000 | \omega(G-x) | | |
| voloshin-hypergraph_FO0900 | 127 | 1.000 | \omega(G)=\omega(G-x) | | |
| voloshin-hypergraph_FO0901 | 127 | 1.000 | |N(x)| \leq \omega(G-x)-1 | | |
| voloshin-hypergraph_FO0902 | 127 | 0.953 | \omega(G)=\omega(G-x)+1 | | |
| voloshin-hypergraph_FO0903 | 127 | 0.953 | |N(x)|=\omega(G-x) | | |
| voloshin-hypergraph_FO0904 | 127 | 0.902 | \overline{G-x} | | |
| voloshin-hypergraph_FO0905 | 127 | 0.993 | C_{2 k+1} | | |
| voloshin-hypergraph_FO0906 | 127 | 0.993 | \bar{C}_{2 k+1} | | |
| voloshin-hypergraph_FO0907 | 128 | 0.999 | P_{5}, C_{4}, C_{6}, K_{4} | | |
| voloshin-hypergraph_FO0908 | 128 | 0.999 | \theta\left(C_{7}\right)>\alpha\left(C_{7}\right) | | |
| voloshin-hypergraph_FO0909 | 128 | 0.829 | \Theta(G) | | |
| voloshin-hypergraph_FO0910 | 128 | 1.000 | \lambda \geq 0 | | |
| voloshin-hypergraph_FO0911 | 128 | 1.000 | |E| | | |
| voloshin-hypergraph_FO0912 | 128 | 1.000 | \chi^{\prime}(G) | | |
| voloshin-hypergraph_FO0913 | 128 | 1.000 | G^{\prime}= | | |
| voloshin-hypergraph_FO0914 | 128 | 1.000 | \left(X^{\prime}, E^{\prime}\right) | | |
| voloshin-hypergraph_FO0915 | 128 | 1.000 | X^{\prime}=E | | |
| voloshin-hypergraph_FO0916 | 129 | 1.000 | G^{\prime}=L(G) | | |
| voloshin-hypergraph_FO0917 | 129 | 1.000 | P(L(G), \lambda)=\lambda(\lambda-1)(\lambda-2)^{2}(\lambda-3) | | |
| voloshin-hypergraph_FO0918 | 129 | 1.000 | \{b, c, d, e\} | | |
| voloshin-hypergraph_FO0919 | 129 | 1.000 | \chi^{\prime}(G)=4=\chi(L(G)) | | |
| voloshin-hypergraph_FO0920 | 129 | 1.000 | \chi^{\prime}(G)=\chi(L(G)) | | |
| voloshin-hypergraph_FO0921 | 129 | 1.000 | \chi^{\prime}(G) \geq \Delta(G) | | |
| voloshin-hypergraph_FO0922 | 129 | 1.000 | \Delta | | |
| voloshin-hypergraph_FO0923 | 129 | 1.000 | \chi^{\prime} | | |
| voloshin-hypergraph_FO0924 | 129 | 0.996 | \boldsymbol{\chi} | | |
| voloshin-hypergraph_FO0925 | 129 | 0.996 | \boldsymbol{\chi} \geq \boldsymbol{\omega} | | |
| voloshin-hypergraph_FO0926 | 129 | 1.000 | C_{2 k} | | |
| voloshin-hypergraph_FO0927 | 129 | 0.990 | \Delta+1 | | |
| voloshin-hypergraph_FO0928 | 129 | 1.000 | y_{0} | | |
| voloshin-hypergraph_FO0929 | 129 | 1.000 | x y_{0} | | |
| voloshin-hypergraph_FO0930 | 130 | 1.000 | c_{0} | | |
| voloshin-hypergraph_FO0931 | 130 | 1.000 | c_{1} | | |
| voloshin-hypergraph_FO0932 | 130 | 1.000 | x y_{k} | | |
| voloshin-hypergraph_FO0933 | 130 | 1.000 | c_{i} | | |
| voloshin-hypergraph_FO0934 | 130 | 1.000 | x y_{1} | | |
| voloshin-hypergraph_FO0935 | 130 | 1.000 | c_{2} | | |
| voloshin-hypergraph_FO0936 | 130 | 1.000 | y_{1} | | |
| voloshin-hypergraph_FO0937 | 130 | 1.000 | x y_{2} | | |
| voloshin-hypergraph_FO0938 | 130 | 1.000 | c_{3} | | |
| voloshin-hypergraph_FO0939 | 130 | 1.000 | y_{2} | | |
| voloshin-hypergraph_FO0940 | 130 | 1.000 | x y_{3} | | |
| voloshin-hypergraph_FO0941 | 130 | 1.000 | c_{4} | | |
| voloshin-hypergraph_FO0942 | 130 | 1.000 | y_{3} | | |
| voloshin-hypergraph_FO0943 | 130 | 0.999 | \bar{c}_{i} | | |
| voloshin-hypergraph_FO0944 | 130 | 0.999 | c_{l+1} | | |
| voloshin-hypergraph_FO0945 | 130 | 1.000 | y_{l} | | |
| voloshin-hypergraph_FO0946 | 130 | 1.000 | x y_{i} | | |
| voloshin-hypergraph_FO0947 | 130 | 1.000 | c_{i+1}, i=1,2, \ldots, l | | |
| voloshin-hypergraph_FO0948 | 130 | 1.000 | c_{1}, c_{2}, c_{3}, \ldots | | |
| voloshin-hypergraph_FO0949 | 130 | 1.000 | c_{l+1}=c_{k} | | |
| voloshin-hypergraph_FO0950 | 130 | 1.000 | 1 \leq k \leq l | | |
| voloshin-hypergraph_FO0951 | 131 | 1.000 | c_{k} | | |
| voloshin-hypergraph_FO0952 | 131 | 1.000 | y_{k} | | |
| voloshin-hypergraph_FO0953 | 131 | 1.000 | y_{k-1} | | |
| voloshin-hypergraph_FO0954 | 131 | 1.000 | x y_{k-1} | | |
| voloshin-hypergraph_FO0955 | 131 | 1.000 | x, P | | |
| voloshin-hypergraph_FO0956 | 131 | 1.000 | \chi^{\prime}(G)= | | |
| voloshin-hypergraph_FO0957 | 131 | 0.998 | \chi^{\prime}(G)=\Delta(G)+1 | | |
| voloshin-hypergraph_FO0958 | 131 | 1.000 | \mu(G) | | |
| voloshin-hypergraph_FO0959 | 131 | 1.000 | \Delta(G) \leq \chi^{\prime}(G) \leq \Delta(G)+\mu(G) | | |
| voloshin-hypergraph_FO0961 | 131 | 1.000 | \chi^{\prime}(G)=\Delta(G)+\mu(G) | | |
| voloshin-hypergraph_FO0962 | 131 | 1.000 | \mu=1 | | |
| voloshin-hypergraph_FO0963 | 131 | 1.000 | \chi^{\prime}(G)=\Delta(G) | | |
| voloshin-hypergraph_FO0964 | 131 | 1.000 | K_{n}, C_{n}, W_{n}, K_{m, n} | | |
| voloshin-hypergraph_FO0965 | 131 | 1.000 | m, n \geq 3 | | |
| voloshin-hypergraph_FO0966 | 132 | 1.000 | \chi^{\prime}=4 | | |
| voloshin-hypergraph_FO0967 | 132 | 0.988 | k \leq \lambda | | |
| voloshin-hypergraph_FO0968 | 132 | 0.881 | \boldsymbol{k} | | |
| voloshin-hypergraph_FO0969 | 132 | 1.000 | \bar{\chi}^{\prime}(G) | | |
| voloshin-hypergraph_FO0970 | 132 | 0.988 | \bar{\chi}^{\prime}(G)=3 | | |
| voloshin-hypergraph_FO0971 | 132 | 0.990 | \bar{\chi}^{\prime}(G)=1 | | |
| voloshin-hypergraph_FO0972 | 132 | 1.000 | \Delta(G) \leq 2 | | |
| voloshin-hypergraph_FO0973 | 132 | 0.876 | \Delta(G) \geq 3 | | |
| voloshin-hypergraph_FO0974 | 133 | 0.999 | \bar{\chi}^{\prime}(G) \geq 2 | | |
| voloshin-hypergraph_FO0975 | 133 | 0.996 | \left\{C_{1}, C_{2}, \ldots, C_{k}\right\} | | |
| voloshin-hypergraph_FO0976 | 133 | 0.996 | C_{i} | | |
| voloshin-hypergraph_FO0977 | 133 | 1.000 | G_{i}=\left(X_{i}, C_{i}\right) | | |
| voloshin-hypergraph_FO0978 | 133 | 1.000 | X_{i} | | |
| voloshin-hypergraph_FO0979 | 133 | 0.839 | \left(\bar{\chi}^{\prime}(G)+1\right) | | |
| voloshin-hypergraph_FO0980 | 133 | 0.996 | 1 \leq i \leq | | |
| voloshin-hypergraph_FO0981 | 133 | 0.939 | G_{j} | | |
| voloshin-hypergraph_FO0982 | 134 | 1.000 | G_{k} | | |
| voloshin-hypergraph_FO0983 | 134 | 1.000 | G_{l} s | | |
| voloshin-hypergraph_FO0984 | 134 | 0.998 | c^{\prime} | | |
| voloshin-hypergraph_FO0985 | 134 | 0.998 | c^{\prime} \leq c | | |
| voloshin-hypergraph_FO0986 | 134 | 1.000 | |X|=n,|E|=m | | |
| voloshin-hypergraph_FO0987 | 135 | 1.000 | \bar{\chi}^{\prime}(G) \leq c+m-n+p | | |
| voloshin-hypergraph_FO0988 | 135 | 0.999 | G_{i}, 1 \leq i \leq \bar{\chi}^{\prime}(G) | | |
| voloshin-hypergraph_FO0989 | 135 | 1.000 | v^{\prime} | | |
| voloshin-hypergraph_FO0990 | 135 | 1.000 | G_{l} | | |
| voloshin-hypergraph_FO0991 | 135 | 0.419 | G_{k} \mathrm{~s} | | |
| voloshin-hypergraph_FO0992 | 135 | 0.915 | n-v^{\prime}-p | | |
| voloshin-hypergraph_FO0993 | 135 | 0.973 | m^{\prime} | | |
| voloshin-hypergraph_FO0994 | 135 | 1.000 | m-m^{\prime} | | |
| voloshin-hypergraph_FO0995 | 135 | 0.995 | \bar{\chi}^{\prime}(G) \geq c+m-n+p | | |
| voloshin-hypergraph_FO0996 | 135 | 1.000 | C_{1}, \ldots, C_{c} | | |
| voloshin-hypergraph_FO0997 | 135 | 1.000 | A_{0} | | |
| voloshin-hypergraph_FO0998 | 135 | 0.999 | 1, \ldots, c | | |
| voloshin-hypergraph_FO0999 | 135 | 0.999 | m\left(A_{0}\right)= | | |
| voloshin-hypergraph_FO1000 | 135 | 1.000 | n\left(A_{0}\right) | | |
| voloshin-hypergraph_FO1001 | 135 | 1.000 | p\left(A_{0}\right)=0 | | |
| voloshin-hypergraph_FO1002 | 135 | 1.000 | c+m\left(A_{0}\right)-n\left(A_{0}\right)+p\left(A_{0}\right) | | |
| voloshin-hypergraph_FO1003 | 135 | 1.000 | \bar{\chi}^{\prime}\left(A_{0}\right) \geq c+m\left(A_{0}\right)-n\left(A_{0}\right)+p\left(A_{0}\right) | | |
| voloshin-hypergraph_FO1004 | 135 | 1.000 | x=y | | |
| voloshin-hypergraph_FO1005 | 135 | 1.000 | A_{1} | | |
| voloshin-hypergraph_FO1006 | 136 | 1.000 | A_{2}, A_{3}, \ldots | | |
| voloshin-hypergraph_FO1007 | 136 | 1.000 | c=1, m=5, n=4 | | |
| voloshin-hypergraph_FO1008 | 136 | 1.000 | p=1 | | |
| voloshin-hypergraph_FO1009 | 136 | 1.000 | c=0 | | |
| voloshin-hypergraph_FO1010 | 136 | 1.000 | \bar{\chi}^{\prime}(G)=c+m-n+p | | |
| voloshin-hypergraph_FO1011 | 137 | 1.000 | C_{n}, W_{n}, K_{n}, K_{m, n} | | |
| voloshin-hypergraph_FO1012 | 137 | 1.000 | m, n \geq 2 | | |
| voloshin-hypergraph_FO1013 | 137 | 1.000 | K_{n}, n \geq 5 | | |
| voloshin-hypergraph_FO1014 | 139 | 1.000 | x_{0}, e_{1}, x_{1}, e_{2}, \ldots, e_{k}, x_{k} | | |
| voloshin-hypergraph_FO1015 | 139 | 0.999 | x_{k} | | |
| voloshin-hypergraph_FO1016 | 139 | 0.999 | \left(x_{0}, x_{k}\right) | | |
| voloshin-hypergraph_FO1017 | 139 | 0.999 | x_{0}=x_{k} | | |
| voloshin-hypergraph_FO1019 | 140 | 0.562 | \Sigma_{i=1}^{n} d\left(x_{i}\right)=2 m | | |
| voloshin-hypergraph_FO1020 | 140 | 1.000 | k / 2 | | |
| voloshin-hypergraph_FO1021 | 141 | 1.000 | |X|=n \geq 3 | | |
| voloshin-hypergraph_FO1022 | 141 | 1.000 | d\left(x_{1}\right)+d\left(x_{n}\right) \geq n | | |
| voloshin-hypergraph_FO1023 | 141 | 1.000 | d\left(x_{1}\right) \leq n-2 | | |
| voloshin-hypergraph_FO1024 | 141 | 1.000 | d\left(x_{n}\right) \leq | | |
| voloshin-hypergraph_FO1025 | 141 | 1.000 | n-3 | | |
| voloshin-hypergraph_FO1026 | 142 | 0.984 | \left(x_{i}, x_{i+1}\right) | | |
| voloshin-hypergraph_FO1027 | 142 | 0.984 | x_{i+1} | | |
| voloshin-hypergraph_FO1028 | 142 | 1.000 | n / 2 | | |
| voloshin-hypergraph_FO1029 | 142 | 1.000 | d(x)+d(y) \geq n | | |
| voloshin-hypergraph_FO1030 | 142 | 1.000 | \overline{C_{7}} | | |
| voloshin-hypergraph_FO1031 | 142 | 1.000 | \overline{C_{8}} | | |
| voloshin-hypergraph_FO1032 | 143 | 1.000 | N=(X, A) | | |
| voloshin-hypergraph_FO1033 | 143 | 1.000 | a \in A | | |
| voloshin-hypergraph_FO1034 | 143 | 1.000 | c(a) | | |
| voloshin-hypergraph_FO1035 | 143 | 1.000 | y \in X | | |
| voloshin-hypergraph_FO1036 | 143 | 0.666 | (y, z) | | |
| voloshin-hypergraph_FO1037 | 143 | 0.666 | N | | |
| voloshin-hypergraph_FO1038 | 143 | 1.000 | u \in X | | |
| voloshin-hypergraph_FO1039 | 143 | 1.000 | v \in X | | |
| voloshin-hypergraph_FO1040 | 143 | 0.958 | F | | |
| voloshin-hypergraph_FO1041 | 143 | 0.958 | f(a) | | |
| voloshin-hypergraph_FO1042 | 143 | 0.991 | f(a) \leq c(a) | | |
| voloshin-hypergraph_FO1043 | 143 | 0.999 | u | | |
| voloshin-hypergraph_FO1044 | 143 | 0.999 | v | | |
| voloshin-hypergraph_FO1045 | 143 | 1.000 | f(a)=c(a) | | |
| voloshin-hypergraph_FO1046 | 143 | 1.000 | f(a)<c(a) | | |
| voloshin-hypergraph_FO1047 | 143 | 1.000 | (u, x) | | |
| voloshin-hypergraph_FO1048 | 143 | 1.000 | (x, v) | | |
| voloshin-hypergraph_FO1049 | 143 | 0.798 | u=x_{0} \rightarrow x_{1} \rightarrow x_{2} \rightarrow \cdots \rightarrow x_{k} | | |
| voloshin-hypergraph_FO1050 | 143 | 0.798 | \left(x_{i+1}, x_{i}\right) | | |
| voloshin-hypergraph_FO1051 | 143 | 0.982 | i=0,1, \ldots, k-1 | | |
| voloshin-hypergraph_FO1052 | 143 | 1.000 | u \in Y | | |
| voloshin-hypergraph_FO1053 | 143 | 1.000 | Z=X \backslash Y | | |
| voloshin-hypergraph_FO1054 | 143 | 1.000 | v \in Z | | |
| voloshin-hypergraph_FO1055 | 143 | 1.000 | v \in Y | | |
| voloshin-hypergraph_FO1056 | 143 | 1.000 | u=x_{0} \rightarrow x_{1} \rightarrow | | |
| voloshin-hypergraph_FO1057 | 143 | 0.975 | x_{2} \rightarrow \cdots \rightarrow x_{k}=v | | |
| voloshin-hypergraph_FO1058 | 143 | 0.975 | \delta>0 | | |
| voloshin-hypergraph_FO1059 | 144 | 0.777 | x_{i}, x_{i+1} | | |
| voloshin-hypergraph_FO1060 | 144 | 0.997 | \delta | | |
| voloshin-hypergraph_FO1061 | 144 | 1.000 | Z | | |
| voloshin-hypergraph_FO1062 | 144 | 0.980 | (0,3) | | |
| voloshin-hypergraph_FO1063 | 144 | 0.980 | \left(u, x_{1}\right) | | |
| voloshin-hypergraph_FO1064 | 144 | 0.980 | F_{0} | | |
| voloshin-hypergraph_FO1065 | 144 | 0.922 | \left(x_{3}, x_{1}\right) | | |
| voloshin-hypergraph_FO1066 | 144 | 1.000 | (1,1) | | |
| voloshin-hypergraph_FO1067 | 144 | 0.815 | F_{1} | | |
| voloshin-hypergraph_FO1068 | 144 | 0.815 | u, x_{1} | | |
| voloshin-hypergraph_FO1069 | 144 | 0.971 | \left(x_{1}, x_{3}\right) | | |
| voloshin-hypergraph_FO1070 | 144 | 0.971 | \left(x_{3}, v\right) | | |
| voloshin-hypergraph_FO1071 | 144 | 1.000 | F_{2} | | |
| voloshin-hypergraph_FO1072 | 144 | 1.000 | F_{3} | | |
| voloshin-hypergraph_FO1073 | 144 | 1.000 | F_{4} | | |
| voloshin-hypergraph_FO1074 | 144 | 0.522 | \left(u, x_{1}\right),\left(x_{3}, x_{1}\right) | | |
| voloshin-hypergraph_FO1075 | 144 | 0.546 | x_{4}, x_{2} | | |
| voloshin-hypergraph_FO1076 | 146 | 1.000 | W_{7} | | |
| voloshin-hypergraph_FO1077 | 151 | 0.967 | \mathcal{D}=\left\{D_{1}, D_{2}, \ldots, D_{m}\right\} | | |
| voloshin-hypergraph_FO1078 | 151 | 1.000 | \mathcal{H}=(X, \mathcal{D}) | | |
| voloshin-hypergraph_FO1079 | 151 | 1.000 | V(\mathcal{H}) | | |
| voloshin-hypergraph_FO1080 | 151 | 1.000 | \mathcal{D}(\mathcal{H}) | | |
| voloshin-hypergraph_FO1081 | 152 | 1.000 | n(\mathcal{H}) | | |
| voloshin-hypergraph_FO1082 | 152 | 0.999 | D_{1}, D_{2}, \ldots, D_{m} | | |
| voloshin-hypergraph_FO1083 | 152 | 1.000 | m(\mathcal{H}) | | |
| voloshin-hypergraph_FO1084 | 152 | 1.000 | x_{i} \in X | | |
| voloshin-hypergraph_FO1085 | 152 | 1.000 | D_{j} \in \mathcal{D} | | |
| voloshin-hypergraph_FO1086 | 152 | 0.996 | \mathcal{D}(x), x \in X | | |
| voloshin-hypergraph_FO1087 | 152 | 0.996 | |\mathcal{D}(x)| | | |
| voloshin-hypergraph_FO1088 | 152 | 1.000 | \left|D_{i}\right| | | |
| voloshin-hypergraph_FO1089 | 152 | 1.000 | D_{i} | | |
| voloshin-hypergraph_FO1090 | 152 | 1.000 | \mathcal{H} | | |
| voloshin-hypergraph_FO1091 | 152 | 1.000 | r \geq 0 | | |
| voloshin-hypergraph_FO1092 | 152 | 0.998 | \left|D_{i}\right|=2 | | |
| voloshin-hypergraph_FO1093 | 152 | 0.998 | D_{i} \in \mathcal{D} | | |
| voloshin-hypergraph_FO1094 | 152 | 0.998 | \mathcal{H}_{1} | | |
| voloshin-hypergraph_FO1095 | 152 | 0.998 | \mathcal{H}_{2} | | |
| voloshin-hypergraph_FO1096 | 155 | 1.000 | I(\mathcal{H}) | | |
| voloshin-hypergraph_FO1097 | 156 | 1.000 | \mathcal{D}=\left\{D_{1}, D_{2}, \ldots\right. | | |
| voloshin-hypergraph_FO1098 | 156 | 1.000 | \left.D_{m}\right\} | | |
| voloshin-hypergraph_FO1099 | 156 | 1.000 | \mathcal{H}^{*}=(Y, Z) | | |
| voloshin-hypergraph_FO1100 | 156 | 1.000 | Y=\left\{d_{1}, d_{2}, \ldots, d_{m}\right\} | | |
| voloshin-hypergraph_FO1101 | 156 | 1.000 | I\left(\mathcal{H}^{*}\right) | | |
| voloshin-hypergraph_FO1102 | 156 | 1.000 | I^{*} | | |
| voloshin-hypergraph_FO1103 | 156 | 1.000 | \mathcal{H}^{*} | | |
| voloshin-hypergraph_FO1104 | 156 | 1.000 | I\left(\mathcal{H}^{*}\right)=I^{*}(\mathcal{H}) | | |
| voloshin-hypergraph_FO1105 | 156 | 1.000 | \left(\mathcal{H}^{*}\right)^{*}=\mathcal{H} | | |
| voloshin-hypergraph_FO1106 | 156 | 1.000 | \Delta(\mathcal{H})=r\left(\mathcal{H}^{*}\right) | | |
| voloshin-hypergraph_FO1107 | 156 | 0.869 | I(\mathcal{H}) \Rightarrow | | |
| voloshin-hypergraph_FO1108 | 156 | 0.869 | I^{*}(\mathcal{H}) \Rightarrow | | |
| voloshin-hypergraph_FO1109 | 156 | 1.000 | B(\mathcal{H})=(X, \mathcal{D} ; E) | | |
| voloshin-hypergraph_FO1110 | 156 | 1.000 | X \cup \mathcal{D} | | |
| voloshin-hypergraph_FO1111 | 156 | 1.000 | B(\mathcal{H}) | | |
| voloshin-hypergraph_FO1112 | 156 | 1.000 | B\left(\mathcal{H}^{*}\right) | | |
| voloshin-hypergraph_FO1113 | 156 | 1.000 | D_{1} | | |
| voloshin-hypergraph_FO1114 | 156 | 1.000 | \left|D_{1}\right|=1 | | |
| voloshin-hypergraph_FO1115 | 156 | 1.000 | D_{2} | | |
| voloshin-hypergraph_FO1116 | 156 | 1.000 | D_{3} | | |
| voloshin-hypergraph_FO1117 | 156 | 0.817 | d_{1} | | |
| voloshin-hypergraph_FO1119 | 158 | 1.000 | B(\mathcal{H})= | | |
| voloshin-hypergraph_FO1120 | 158 | 1.000 | (X, \mathcal{D} ; E) | | |
| voloshin-hypergraph_FO1121 | 159 | 1.000 | n \times n | | |
| voloshin-hypergraph_FO1122 | 159 | 1.000 | A=\left(a_{i j}\right) | | |
| voloshin-hypergraph_FO1123 | 159 | 1.000 | A(\mathcal{H}) | | |
| voloshin-hypergraph_FO1124 | 159 | 1.000 | (0,1) | | |
| voloshin-hypergraph_FO1125 | 159 | 1.000 | B(B(\mathcal{H})) | | |
| voloshin-hypergraph_FO1126 | 159 | 1.000 | B(G) | | |
| voloshin-hypergraph_FO1127 | 159 | 1.000 | E_{n}, K_{n}, P_{n}, C_{n} | | |
| voloshin-hypergraph_FO1128 | 159 | 1.000 | W_{n}, n=3,4,5,6,7 | | |
| voloshin-hypergraph_FO1129 | 160 | 1.000 | 0 \leq r \leq n | | |
| voloshin-hypergraph_FO1130 | 160 | 1.000 | K_{n}^{r}=(X, \mathcal{D}) | | |
| voloshin-hypergraph_FO1131 | 160 | 1.000 | \mathcal{D}\left(K_{n}^{r}\right) | | |
| voloshin-hypergraph_FO1132 | 160 | 0.999 | K_{n}^{2} | | |
| voloshin-hypergraph_FO1133 | 160 | 1.000 | K_{n}^{r} | | |
| voloshin-hypergraph_FO1134 | 160 | 1.000 | K_{n}^{r}=\left(X, K_{n}^{r}\right) | | |
| voloshin-hypergraph_FO1135 | 160 | 1.000 | K_{4}^{0} | | |
| voloshin-hypergraph_FO1136 | 160 | 1.000 | 1+4+6+4+1=16=2^{4}=2^{n} | | |
| voloshin-hypergraph_FO1137 | 160 | 1.000 | n \geq 0 | | |
| voloshin-hypergraph_FO1138 | 160 | 1.000 | K_{4}^{3} | | |
| voloshin-hypergraph_FO1139 | 160 | 1.000 | K_{4}^{2} | | |
| voloshin-hypergraph_FO1140 | 160 | 1.000 | \binom{n-1}{r-1} | | |
| voloshin-hypergraph_FO1141 | 160 | 1.000 | x_{0}, x_{1}, x_{2}, \ldots, x_{t-1} | | |
| voloshin-hypergraph_FO1142 | 160 | 1.000 | D_{0}, D_{1}, D_{2}, \ldots, D_{t-1} | | |
| voloshin-hypergraph_FO1143 | 160 | 1.000 | x_{i}, x_{i+1} \in D_{i}, i=0,1, \ldots, t-1 | | |
| voloshin-hypergraph_FO1144 | 160 | 1.000 | x_{t} | | |
| voloshin-hypergraph_FO1145 | 160 | 1.000 | \left(x_{0}, x_{t}\right) | | |
| voloshin-hypergraph_FO1146 | 160 | 1.000 | x_{t}=x_{0} | | |
| voloshin-hypergraph_FO1147 | 160 | 0.831 | \mu_{1}=1 D_{2} 2 D_{4} 3 D_{5} 5 | | |
| voloshin-hypergraph_FO1148 | 160 | 1.000 | \mu_{2}=1 D_{2} 2 D_{4} 3 D_{5} 4 D_{3} 1 | | |
| voloshin-hypergraph_FO1149 | 160 | 1.000 | \mathcal{H}, \mathcal{H}^{*} | | |
| voloshin-hypergraph_FO1150 | 161 | 1.000 | K_{4}^{1} | | |
| voloshin-hypergraph_FO1151 | 161 | 1.000 | K_{4}^{2}, K_{4}^{3} | | |
| voloshin-hypergraph_FO1152 | 161 | 1.000 | K_{4}^{4} | | |
| voloshin-hypergraph_FO1153 | 161 | 1.000 | \geq 2 | | |
| voloshin-hypergraph_FO1154 | 161 | 1.000 | K_{n_{1}, n_{2}, \ldots, n_{r}}^{r} | | |
| voloshin-hypergraph_FO1155 | 161 | 1.000 | n_{i} | | |
| voloshin-hypergraph_FO1156 | 161 | 0.992 | \mathcal{H}^{\prime}=\left(X^{\prime}, \mathcal{D}^{\prime}\right) | | |
| voloshin-hypergraph_FO1157 | 161 | 0.992 | \mathcal{H} \cong \mathcal{H}^{\prime} | | |
| voloshin-hypergraph_FO1158 | 161 | 0.999 | \mathcal{D}^{\prime} | | |
| voloshin-hypergraph_FO1159 | 161 | 0.999 | x \in D | | |
| voloshin-hypergraph_FO1160 | 162 | 1.000 | x^{\prime} \in X^{\prime} | | |
| voloshin-hypergraph_FO1161 | 162 | 1.000 | D^{\prime} \in \mathcal{D}^{\prime} | | |
| voloshin-hypergraph_FO1162 | 162 | 1.000 | x^{\prime} \in D^{\prime} | | |
| voloshin-hypergraph_FO1163 | 162 | 1.000 | K_{4}^{3}, K_{5}^{3}, K_{5}^{1}, K_{6}^{5} | | |
| voloshin-hypergraph_FO1164 | 162 | 1.000 | K_{7}^{4} | | |
| voloshin-hypergraph_FO1165 | 162 | 1.000 | K_{1,2,3}^{3} | | |
| voloshin-hypergraph_FO1166 | 162 | 1.000 | n_{1}, n_{2}, n_{3} \geq 1 | | |
| voloshin-hypergraph_FO1167 | 162 | 1.000 | K_{n_{1}, n_{2}, n_{3}}^{3} | | |
| voloshin-hypergraph_FO1168 | 162 | 1.000 | \mathcal{D}(x) | | |
| voloshin-hypergraph_FO1169 | 162 | 1.000 | \mathcal{D}_{1}=\mathcal{D}-\mathcal{D}(x) | | |
| voloshin-hypergraph_FO1170 | 162 | 0.996 | \mathcal{H}_{1}=\left(X_{1}, \mathcal{D}_{1}\right) | | |
| voloshin-hypergraph_FO1171 | 162 | 0.996 | \mathcal{H}_{1}=\mathcal{H}-x | | |
| voloshin-hypergraph_FO1172 | 163 | 1.000 | \mathcal{H}= | | |
| voloshin-hypergraph_FO1173 | 163 | 1.000 | (X, \mathcal{D}) | | |
| voloshin-hypergraph_FO1174 | 164 | 1.000 | \mathcal{H}_{1}=\mathcal{H}-D | | |
| voloshin-hypergraph_FO1175 | 165 | 0.974 | D^{\prime} \in \mathcal{D} | | |
| voloshin-hypergraph_FO1176 | 165 | 0.974 | D \cap D^{\prime} \neq \emptyset | | |
| voloshin-hypergraph_FO1177 | 165 | 1.000 | \mathcal{H}_{1}^{*} | | |
| voloshin-hypergraph_FO1178 | 166 | 0.997 | \{7,11,12\} | | |
| voloshin-hypergraph_FO1179 | 166 | 0.997 | \{3,5,9\} | | |
| voloshin-hypergraph_FO1180 | 167 | 1.000 | \mathcal{H}^{\prime}= | | |
| voloshin-hypergraph_FO1181 | 167 | 0.983 | \left(X^{\prime}, \mathcal{D}^{\prime}\right) | | |
| voloshin-hypergraph_FO1182 | 167 | 0.983 | \mathcal{D}^{\prime} \subseteq \mathcal{D} | | |
| voloshin-hypergraph_FO1183 | 167 | 1.000 | \mathcal{H}^{\prime} \subseteq \mathcal{H} | | |
| voloshin-hypergraph_FO1184 | 167 | 1.000 | \mathcal{H}^{\prime} | | |
| voloshin-hypergraph_FO1185 | 167 | 0.999 | \mathcal{D}-\mathcal{D}^{\prime} | | |
| voloshin-hypergraph_FO1186 | 167 | 0.978 | \mathcal{H}: \mathcal{H}_{1} | | |
| voloshin-hypergraph_FO1187 | 167 | 0.996 | \mathcal{H}_{Y} | | |
| voloshin-hypergraph_FO1188 | 167 | 0.996 | Y=\{2,3,4\} | | |
| voloshin-hypergraph_FO1189 | 167 | 0.996 | \mathcal{H}_{1}=\mathcal{H}_{Y} | | |
| voloshin-hypergraph_FO1190 | 167 | 1.000 | \mathcal{H}^{\prime}=\left(X, \mathcal{D}^{\prime}\right) | | |
| voloshin-hypergraph_FO1191 | 167 | 0.743 | \alpha(\mathcal{H}) | | |
| voloshin-hypergraph_FO1192 | 167 | 0.946 | 1 \leq \alpha(\mathcal{H}) \leq|X| | | |
| voloshin-hypergraph_FO1193 | 167 | 0.976 | \alpha(\mathcal{H})=3 | | |
| voloshin-hypergraph_FO1194 | 168 | 1.000 | |S \cap D| \leq 1 | | |
| voloshin-hypergraph_FO1195 | 168 | 1.000 | D \in | | |
| voloshin-hypergraph_FO1196 | 168 | 1.000 | \bar{\alpha}(\mathcal{H}) | | |
| voloshin-hypergraph_FO1197 | 168 | 1.000 | G, \alpha(G)=\bar{\alpha}(G) | | |
| voloshin-hypergraph_FO1198 | 168 | 1.000 | |T \cap D| \geq 1 | | |
| voloshin-hypergraph_FO1199 | 168 | 1.000 | \tau(\mathcal{H}) | | |
| voloshin-hypergraph_FO1200 | 168 | 1.000 | S=X-T | | |
| voloshin-hypergraph_FO1201 | 168 | 1.000 | \tau=2 | | |
| voloshin-hypergraph_FO1202 | 168 | 0.822 | \alpha(\mathcal{H})+\tau(\mathcal{H})=3+2=5=|X| | | |
| voloshin-hypergraph_FO1203 | 168 | 0.995 | \mathcal{V}(\mathcal{H}) | | |
| voloshin-hypergraph_FO1204 | 168 | 0.956 | \nu(\mathcal{H})=\bar{\alpha}\left(\mathcal{H}^{*}\right) | | |
| voloshin-hypergraph_FO1205 | 168 | 0.940 | \{1,2,5\} | | |
| voloshin-hypergraph_FO1206 | 168 | 0.940 | \mathcal{V}(\mathcal{H})=2 | | |
| voloshin-hypergraph_FO1207 | 168 | 0.983 | \tau(\mathcal{H}) \geq 2=v(\mathcal{H}) | | |
| voloshin-hypergraph_FO1208 | 168 | 0.983 | \tau(\mathcal{H})=v(\mathcal{H}), \mathcal{H} | | |
| voloshin-hypergraph_FO1209 | 169 | 1.000 | \rho(\mathcal{H}) | | |
| voloshin-hypergraph_FO1210 | 169 | 1.000 | \rho(\mathcal{H})=\bar{\alpha}(\mathcal{H}) | | |
| voloshin-hypergraph_FO1211 | 169 | 0.522 | \rho(\mathcal{H})=2 | | |
| voloshin-hypergraph_FO1212 | 169 | 0.522 | \bar{\alpha}(\mathcal{H})=2 | | |
| voloshin-hypergraph_FO1213 | 169 | 0.991 | \tau=3>2=\nu | | |
| voloshin-hypergraph_FO1214 | 169 | 0.991 | \rho=3>\bar{\alpha}=\alpha=2 | | |
| voloshin-hypergraph_FO1215 | 169 | 1.000 | X^{\prime}=\{1,2,3,4,5,7,8\} | | |
| voloshin-hypergraph_FO1216 | 169 | 1.000 | \mathcal{D}^{\prime}= | | |
| voloshin-hypergraph_FO1217 | 169 | 0.997 | v(\mathcal{H}) | | |
| voloshin-hypergraph_FO1218 | 170 | 0.531 | \mathcal{v}(\mathcal{H}) | | |
| voloshin-hypergraph_FO1219 | 170 | 1.000 | L(\mathcal{H}) | | |
| voloshin-hypergraph_FO1220 | 170 | 1.000 | (\mathcal{H})_{2} | | |
| voloshin-hypergraph_FO1221 | 170 | 1.000 | L\left(\mathcal{H}^{*}\right) | | |
| voloshin-hypergraph_FO1222 | 171 | 0.931 | \alpha\left((\mathcal{H})_{2}\right) . \square | | |
| voloshin-hypergraph_FO1225 | 171 | 1.000 | \left(\mathcal{H}^{*}\right)_{2} | | |
| voloshin-hypergraph_FO1226 | 171 | 0.994 | a, b, c, d | | |
| voloshin-hypergraph_FO1230 | 172 | 1.000 | \tau(\mathcal{H})=\theta(L(\mathcal{H})) | | |
| voloshin-hypergraph_FO1231 | 172 | 1.000 | \chi(\overline{L(\mathcal{H})}) | | |
| voloshin-hypergraph_FO1232 | 172 | 1.000 | \overline{L(\mathcal{H})} | | |
| voloshin-hypergraph_FO1233 | 172 | 1.000 | b, c | | |
| voloshin-hypergraph_FO1239 | 172 | 1.000 | Y \subseteq D | | |
| voloshin-hypergraph_FO1240 | 172 | 0.913 | G=(\mathcal{H})_{2} | | |
| voloshin-hypergraph_FO1241 | 172 | 1.000 | Z \subseteq X | | |
| voloshin-hypergraph_FO1242 | 172 | 1.000 | Y \subseteq Z | | |
| voloshin-hypergraph_FO1243 | 172 | 1.000 | G_{Z} | | |
| voloshin-hypergraph_FO1244 | 172 | 1.000 | Z=D | | |
| voloshin-hypergraph_FO1245 | 173 | 1.000 | \mathcal{C} | | |
| voloshin-hypergraph_FO1246 | 173 | 1.000 | \mathcal{D}^{\prime}=\mathcal{C} | | |
| voloshin-hypergraph_FO1247 | 173 | 1.000 | \mathcal{D}^{\prime} \subseteq \mathcal{C} | | |
| voloshin-hypergraph_FO1248 | 173 | 1.000 | D \in \mathcal{D}^{\prime} | | |
| voloshin-hypergraph_FO1249 | 173 | 0.615 | G_{D} | | |
| voloshin-hypergraph_FO1250 | 173 | 0.615 | C \in C | | |
| voloshin-hypergraph_FO1251 | 173 | 0.615 | D \subseteq C | | |
| voloshin-hypergraph_FO1252 | 173 | 1.000 | C \subseteq D^{\prime} | | |
| voloshin-hypergraph_FO1253 | 173 | 0.973 | D \subseteq C \subseteq D^{\prime} | | |
| voloshin-hypergraph_FO1254 | 173 | 0.973 | D=C=D^{\prime} | | |
| voloshin-hypergraph_FO1255 | 173 | 0.973 | D \in \mathcal{C} | | |
| voloshin-hypergraph_FO1256 | 173 | 1.000 | \mathcal{C} \subseteq \mathcal{D}^{\prime} | | |
| voloshin-hypergraph_FO1257 | 173 | 1.000 | C \in \mathcal{C} | | |
| voloshin-hypergraph_FO1258 | 173 | 1.000 | C \subseteq D | | |
| voloshin-hypergraph_FO1259 | 173 | 1.000 | D \subseteq D^{\prime} | | |
| voloshin-hypergraph_FO1260 | 173 | 1.000 | C^{\prime} | | |
| voloshin-hypergraph_FO1261 | 173 | 1.000 | D^{\prime} \subseteq C^{\prime} | | |
| voloshin-hypergraph_FO1262 | 173 | 1.000 | C \subseteq D^{\prime} \subseteq C^{\prime} | | |
| voloshin-hypergraph_FO1263 | 173 | 1.000 | C=D=C^{\prime} | | |
| voloshin-hypergraph_FO1264 | 173 | 1.000 | C \in \mathcal{D}^{\prime} | | |
| voloshin-hypergraph_FO1265 | 173 | 1.000 | D_{1}, D_{2}, D_{3} | | |
| voloshin-hypergraph_FO1266 | 173 | 1.000 | \left(D_{1} \cap D_{2}\right) \cup\left(D_{1} \cap D_{3}\right) \cup\left(D_{2} \cap D_{3}\right) | | |
| voloshin-hypergraph_FO1267 | 173 | 1.000 | |Y| | | |
| voloshin-hypergraph_FO1268 | 173 | 1.000 | |Y|=1 | | |
| voloshin-hypergraph_FO1269 | 173 | 1.000 | |Y|=2 | | |
| voloshin-hypergraph_FO1270 | 173 | 1.000 | |Y|<k, k \geq 3 | | |
| voloshin-hypergraph_FO1271 | 173 | 1.000 | |Y| \geq 3 | | |
| voloshin-hypergraph_FO1272 | 173 | 1.000 | x_{1}, x_{2}, x_{3} \in Y | | |
| voloshin-hypergraph_FO1273 | 173 | 1.000 | Y_{i}=Y-\left\{x_{i}\right\}, i=1,2,3 | | |
| voloshin-hypergraph_FO1274 | 173 | 1.000 | Y_{i} \subseteq D_{i}, i=1,2,3 | | |
| voloshin-hypergraph_FO1275 | 174 | 1.000 | x_{1}, x_{2}, \ldots, x_{k} | | |
| voloshin-hypergraph_FO1276 | 174 | 0.991 | x_{1}, x_{2}, \ldots, x_{k} \in D | | |
| voloshin-hypergraph_FO1277 | 174 | 0.991 | d \in X_{1}, d \in X_{2}, \ldots | | |
| voloshin-hypergraph_FO1278 | 174 | 1.000 | d \in X_{k} | | |
| voloshin-hypergraph_FO1279 | 174 | 1.000 | d \in X_{1} \cap X_{2} \cap \cdots \cap X_{k} | | |
| voloshin-hypergraph_FO1280 | 175 | 0.996 | \mathcal{H}_{2} \cong \mathcal{H}_{1}^{*} | | |
| voloshin-hypergraph_FO1281 | 175 | 0.999 | \mathcal{H}_{3} | | |
| voloshin-hypergraph_FO1282 | 175 | 0.995 | \mathcal{H} \cong \mathcal{H}^{*} | | |
| voloshin-hypergraph_FO1283 | 175 | 1.000 | \mathcal{H}_{3} \cong \mathcal{H}_{3}^{*} | | |
| voloshin-hypergraph_FO1284 | 175 | 1.000 | n, p, q, r \geq 1 | | |
| voloshin-hypergraph_FO1285 | 175 | 1.000 | P_{n}, C_{n}, W_{n}, E_{n}, K_{n}, K_{p, q, r}^{3} | | |
| voloshin-hypergraph_FO1286 | 175 | 1.000 | n, r \geq 1 | | |
| voloshin-hypergraph_FO1287 | 177 | 1.000 | E_{3} | | |
| voloshin-hypergraph_FO1288 | 178 | 1.000 | L^{\prime} | | |
| voloshin-hypergraph_FO1289 | 178 | 1.000 | T-x | | |
| voloshin-hypergraph_FO1290 | 178 | 1.000 | L^{\prime}=L | | |
| voloshin-hypergraph_FO1291 | 178 | 1.000 | \mathcal{F} \subseteq \mathcal{D} | | |
| voloshin-hypergraph_FO1292 | 178 | 1.000 | D \in \mathcal{F} | | |
| voloshin-hypergraph_FO1293 | 178 | 1.000 | n(T)=|X| | | |
| voloshin-hypergraph_FO1294 | 178 | 1.000 | n(T)-1 | | |
| voloshin-hypergraph_FO1295 | 178 | 1.000 | D_{j} | | |
| voloshin-hypergraph_FO1296 | 178 | 1.000 | \mathcal{F} | | |
| voloshin-hypergraph_FO1297 | 179 | 1.000 | \mathcal{D}(x) \subseteq \mathcal{D}(y) | | |
| voloshin-hypergraph_FO1298 | 179 | 0.975 | \mathcal{H}=(Y, \mathcal{D}) | | |
| voloshin-hypergraph_FO1299 | 179 | 1.000 | n=n(\mathcal{H}) | | |
| voloshin-hypergraph_FO1300 | 179 | 1.000 | n \leq 2 | | |
| voloshin-hypergraph_FO1301 | 179 | 1.000 | n>2 | | |
| voloshin-hypergraph_FO1302 | 179 | 1.000 | \mathcal{H}_{0} | | |
| voloshin-hypergraph_FO1303 | 179 | 1.000 | \left(\mathcal{H}_{0}\right)_{2} | | |
| voloshin-hypergraph_FO1304 | 179 | 0.999 | D_{0} | | |
| voloshin-hypergraph_FO1307 | 179 | 1.000 | D_{0}-\{x\} | | |
| voloshin-hypergraph_FO1309 | 180 | 0.988 | \mathcal{H}_{0}{ }^{*} | | |
| voloshin-hypergraph_FO1310 | 180 | 0.622 | \mathcal{D}^{\prime}=V\left(\mathcal{H}_{0}^{*}\right) | | |
| voloshin-hypergraph_FO1311 | 180 | 0.622 | x^{\prime} \in V\left(\mathcal{H}_{0}\right)= | | |
| voloshin-hypergraph_FO1312 | 180 | 0.852 | \mathcal{D}\left(\mathcal{H}_{0}^{*}\right) | | |
| voloshin-hypergraph_FO1313 | 180 | 0.985 | d_{0} | | |
| voloshin-hypergraph_FO1314 | 180 | 1.000 | \mathcal{H}_{1}{ }^{*} | | |
| voloshin-hypergraph_FO1315 | 180 | 1.000 | \mathcal{D}_{x}^{\prime} | | |
| voloshin-hypergraph_FO1316 | 180 | 0.707 | D \in \mathcal{D}_{\chi}^{\prime} | | |
| voloshin-hypergraph_FO1317 | 180 | 1.000 | \mathcal{H}_{2}^{*} | | |
| voloshin-hypergraph_FO1322 | 180 | 0.997 | D \in \mathcal{D}_{x}^{\prime} | | |
| voloshin-hypergraph_FO1323 | 180 | 1.000 | D \subset D_{0} | | |
| voloshin-hypergraph_FO1324 | 180 | 0.998 | \left(d, d_{0}\right) | | |
| voloshin-hypergraph_FO1325 | 180 | 0.735 | \left(d, d^{\prime}\right) | | |
| voloshin-hypergraph_FO1326 | 180 | 0.735 | d^{\prime} \neq d_{0} | | |
| voloshin-hypergraph_FO1327 | 180 | 1.000 | T_{3} | | |
| voloshin-hypergraph_FO1328 | 181 | 1.000 | \mathcal{H}_{3}^{*} | | |
| voloshin-hypergraph_FO1329 | 181 | 1.000 | d^{\prime} | | |
| voloshin-hypergraph_FO1330 | 181 | 1.000 | \mathcal{H}_{3}^{*}, \mathcal{H}_{4}^{*}, \ldots | | |
| voloshin-hypergraph_FO1331 | 181 | 1.000 | T_{3}, T_{4}, \ldots | | |
| voloshin-hypergraph_FO1332 | 181 | 0.998 | (\mathcal{H})_{2}=L\left(\mathcal{H}^{*}\right) | | |
| voloshin-hypergraph_FO1333 | 181 | 1.000 | R | | |
| voloshin-hypergraph_FO1334 | 182 | 0.995 | \left(\mathcal{H}^{*}\right)_{2}=L(\mathcal{H}) | | |
| voloshin-hypergraph_FO1335 | 183 | 0.831 | A, B, C, D | | |
| voloshin-hypergraph_FO1336 | 183 | 0.997 | G=L\left(\mathcal{H}^{*}\right) | | |
| voloshin-hypergraph_FO1337 | 183 | 0.998 | \alpha | | |
| voloshin-hypergraph_FO1338 | 183 | 1.000 | L(\mathcal{H})=\left(\mathcal{H}^{*}\right)_{2} | | |
| voloshin-hypergraph_FO1339 | 183 | 1.000 | G=L(\mathcal{H}) | | |
| voloshin-hypergraph_FO1340 | 184 | 1.000 | D=\{x\} | | |
| voloshin-hypergraph_FO1341 | 184 | 1.000 | y \in X, y \neq x | | |
| voloshin-hypergraph_FO1342 | 184 | 1.000 | \mathcal{D}(x)=\emptyset | | |
| voloshin-hypergraph_FO1343 | 184 | 0.607 | \mathrm{T}(\mathcal{H})=\mathrm{T}\left(\mathcal{H}_{1}\right) | | |
| voloshin-hypergraph_FO1344 | 184 | 1.000 | \alpha(\mathcal{H})=\alpha\left(\mathcal{H}_{1}\right)+1 | | |
| voloshin-hypergraph_FO1345 | 184 | 0.505 | v(\mathcal{H})=v\left(\mathcal{H}_{1}\right) | | |
| voloshin-hypergraph_FO1346 | 184 | 1.000 | x \notin T | | |
| voloshin-hypergraph_FO1347 | 184 | 0.730 | T_{1}=T-\{X\} | | |
| voloshin-hypergraph_FO1348 | 184 | 0.730 | \left|T_{1}\right|=|T|-1=\tau(\mathcal{H})-1 | | |
| voloshin-hypergraph_FO1349 | 184 | 1.000 | x \in X-T=S | | |
| voloshin-hypergraph_FO1350 | 184 | 1.000 | x \in T_{1} | | |
| voloshin-hypergraph_FO1351 | 184 | 1.000 | T_{2}=\left(T_{1}-\{x\}\right) \cup\{y\} | | |
| voloshin-hypergraph_FO1352 | 184 | 0.844 | \tau(\mathcal{H}) \leq \tau\left(\mathcal{H}_{1}\right) | | |
| voloshin-hypergraph_FO1353 | 184 | 1.000 | \tau(\mathcal{H}) \geq \tau\left(\mathcal{H}_{1}\right) | | |
| voloshin-hypergraph_FO1354 | 184 | 0.996 | \tau(\mathcal{H})=\tau\left(\mathcal{H}_{1}\right) | | |
| voloshin-hypergraph_FO1355 | 184 | 0.966 | \alpha(\mathcal{H})+\tau(\mathcal{H})=|X|, \alpha\left(\mathcal{H}_{1}\right)+\tau\left(\mathcal{H}_{1}\right)=|X|-1 | | |
| voloshin-hypergraph_FO1356 | 184 | 0.482 | \boldsymbol{\alpha}(\boldsymbol{\mathcal { H }})=\boldsymbol{\alpha}\left(\mathcal{H}_{1}\right)+1 | | |
| voloshin-hypergraph_FO1357 | 184 | 0.511 | \mathcal{V}(\mathcal{H}) \leq \mathcal{v}\left(\mathcal{H}_{1}\right) | | |
| voloshin-hypergraph_FO1358 | 184 | 0.827 | \mathcal{V}(\mathcal{H}) \geq \mathcal{V}\left(\mathcal{H}_{1}\right) | | |
| voloshin-hypergraph_FO1359 | 185 | 0.998 | L(\mathcal{H})= | | |
| voloshin-hypergraph_FO1360 | 185 | 1.000 | L\left(\mathcal{H}_{1}\right) | | |
| voloshin-hypergraph_FO1361 | 185 | 0.927 | \tau(\mathcal{H})=\tau\left(\mathcal{H}_{1}\right)+1 | | |
| voloshin-hypergraph_FO1362 | 185 | 1.000 | \alpha(\mathcal{H})=\alpha\left(\mathcal{H}_{1}\right) | | |
| voloshin-hypergraph_FO1363 | 185 | 0.804 | v(\mathcal{H})=v\left(\mathcal{H}_{1}\right)+1 | | |
| voloshin-hypergraph_FO1364 | 185 | 1.000 | \{x\} \in \mathcal{D} | | |
| voloshin-hypergraph_FO1365 | 185 | 0.989 | T_{1} \subset X_{1}=X-\{x\} | | |
| voloshin-hypergraph_FO1366 | 185 | 0.989 | T_{2}=T_{1} \cup\{x\} \subset X | | |
| voloshin-hypergraph_FO1367 | 185 | 1.000 | \tau(\mathcal{H}) \leq \tau\left(\mathcal{H}_{1}\right)+1 | | |
| voloshin-hypergraph_FO1368 | 185 | 0.999 | T_{0}=T-\{x\} | | |
| voloshin-hypergraph_FO1369 | 185 | 0.999 | \tau(\mathcal{H}) \geq \tau\left(\mathcal{H}_{1}\right)+1 | | |
| voloshin-hypergraph_FO1370 | 185 | 0.999 | \mathcal{F} \cup\{x\} | | |
| voloshin-hypergraph_FO1371 | 185 | 0.999 | \mathcal{V}(\mathcal{H}) \geq \mathcal{V}\left(\mathcal{H}_{1}\right)+1 | | |
| voloshin-hypergraph_FO1372 | 185 | 0.940 | \mathcal{V}(\mathcal{H})-1 \leq \mathcal{V}\left(\mathcal{H}_{1}\right) | | |
| voloshin-hypergraph_FO1373 | 185 | 1.000 | \mathcal{H}=(X, \mathcal{D}),|X| \geq 2 | | |
| voloshin-hypergraph_FO1374 | 186 | 0.786 | \tau=\nu=0 | | |
| voloshin-hypergraph_FO1375 | 186 | 0.753 | \tau=v=1 | | |
| voloshin-hypergraph_FO1376 | 186 | 0.753 | \tau(\mathcal{H})=v(\mathcal{H}) | | |
| voloshin-hypergraph_FO1377 | 186 | 0.974 | \chi=\omega | | |
| voloshin-hypergraph_FO1378 | 186 | 0.974 | \theta=\alpha | | |
| voloshin-hypergraph_FO1379 | 186 | 0.988 | \theta(L(\mathcal{H}))=\alpha(L(\mathcal{H})) | | |
| voloshin-hypergraph_FO1380 | 186 | 0.946 | \nu(\mathcal{H})=\alpha(L(\mathcal{H})) | | |
| voloshin-hypergraph_FO1381 | 186 | 0.650 | \tau(\mathcal{H})=\mathcal{V}(\mathcal{H}) | | |
| voloshin-hypergraph_FO1382 | 187 | 0.930 | \{3\} | | |
| voloshin-hypergraph_FO1383 | 187 | 0.822 | \{2\} | | |
| voloshin-hypergraph_FO1384 | 187 | 0.822 | \mathcal{H}_{4} | | |
| voloshin-hypergraph_FO1385 | 187 | 1.000 | T_{4} | | |
| voloshin-hypergraph_FO1386 | 188 | 1.000 | T=\emptyset, \mathcal{F}=\emptyset | | |
| voloshin-hypergraph_FO1387 | 188 | 0.968 | T, \mathcal{F} | | |
| voloshin-hypergraph_FO1388 | 189 | 1.000 | T=\{1,3,5\} | | |
| voloshin-hypergraph_FO1389 | 189 | 1.000 | \mathcal{F}=\{\{1,6\},\{2,3\},\{4,5\}\} | | |
| voloshin-hypergraph_FO1390 | 189 | 0.769 | \tau(G)=\mathcal{V}(G) | | |
| voloshin-hypergraph_FO1391 | 189 | 0.961 | \tau\left(C_{5}\right)=3>2=v\left(C_{5}\right) | | |
| voloshin-hypergraph_FO1392 | 189 | 0.987 | \tau, \alpha | | |
| voloshin-hypergraph_FO1393 | 189 | 0.772 | \tau(\mathcal{H}), \alpha(\mathcal{H}) | | |
| voloshin-hypergraph_FO1394 | 189 | 0.772 | \nu(\mathcal{H}) | | |
| voloshin-hypergraph_FO1395 | 190 | 0.977 | \wedge(G)= | | |
| voloshin-hypergraph_FO1396 | 190 | 1.000 | m-n+1 | | |
| voloshin-hypergraph_FO1397 | 190 | 1.000 | [\mathcal{H}]_{2} | | |
| voloshin-hypergraph_FO1398 | 190 | 1.000 | \geq 3 | | |
| voloshin-hypergraph_FO1399 | 190 | 1.000 | (\mathcal{H})_{2}=[\mathcal{H}]_{2} | | |
| voloshin-hypergraph_FO1400 | 190 | 1.000 | \bar{T} | | |
| voloshin-hypergraph_FO1401 | 190 | 1.000 | \bar{T}=(T)_{2} | | |
| voloshin-hypergraph_FO1402 | 190 | 1.000 | |D|-1 | | |
| voloshin-hypergraph_FO1403 | 190 | 0.994 | l(\mathcal{H}, T) | | |
| voloshin-hypergraph_FO1404 | 191 | 1.000 | [\mathcal{H}]_{2}=\mathcal{H} | | |
| voloshin-hypergraph_FO1405 | 191 | 0.998 | w(T)=|X|-1=n-1 | | |
| voloshin-hypergraph_FO1406 | 191 | 0.998 | \Lambda(\mathcal{H}, T) | | |
| voloshin-hypergraph_FO1407 | 191 | 1.000 | w(T)=3 | | |
| voloshin-hypergraph_FO1408 | 192 | 0.999 | E_{D} | | |
| voloshin-hypergraph_FO1409 | 192 | 1.000 | c(T, D) | | |
| voloshin-hypergraph_FO1410 | 192 | 1.000 | |D| \geq 2 | | |
| voloshin-hypergraph_FO1411 | 192 | 1.000 | c(T, D)=1 | | |
| voloshin-hypergraph_FO1412 | 192 | 0.960 | T, \Lambda(\mathcal{H}, T) \geq 0 | | |
| voloshin-hypergraph_FO1413 | 192 | 1.000 | l(\mathcal{H}, T) \geq 0 | | |
| voloshin-hypergraph_FO1414 | 192 | 0.913 | \Lambda(\mathcal{H}, T)=0 | | |
| voloshin-hypergraph_FO1415 | 193 | 1.000 | l(\mathcal{H}, T)=0 | | |
| voloshin-hypergraph_FO1416 | 193 | 0.918 | w(T)=\sum_{D \in \mathcal{D}}(|D|-1) | | |
| voloshin-hypergraph_FO1417 | 193 | 0.918 | \wedge(\mathcal{H}, T)=0 | | |
| voloshin-hypergraph_FO1418 | 193 | 1.000 | \overline{T_{1}} | | |
| voloshin-hypergraph_FO1419 | 193 | 1.000 | w\left(T_{1}\right)=w(T) | | |
| voloshin-hypergraph_FO1420 | 193 | 1.000 | x \in X, T | | |
| voloshin-hypergraph_FO1421 | 193 | 1.000 | [\mathcal{H}]_{2}, \mathcal{D}_{T}(x) | | |
| voloshin-hypergraph_FO1422 | 193 | 1.000 | m_{2} | | |
| voloshin-hypergraph_FO1423 | 193 | 1.000 | \mathcal{H}-x | | |
| voloshin-hypergraph_FO1424 | 193 | 1.000 | |\mathcal{D}(x)|=3,\left|\mathcal{D}_{T}(x)\right|=1 | | |
| voloshin-hypergraph_FO1425 | 193 | 1.000 | m_{2}=1 | | |
| voloshin-hypergraph_FO1426 | 194 | 1.000 | [\mathcal{H}]_{2}, x \in X | | |
| voloshin-hypergraph_FO1427 | 194 | 1.000 | \left[\mathcal{H}_{1}\right]_{2} | | |
| voloshin-hypergraph_FO1428 | 194 | 1.000 | T_{1}^{\prime} | | |
| voloshin-hypergraph_FO1429 | 194 | 1.000 | w\left(T_{1}^{\prime}\right) \geq w\left(T_{1}\right) | | |
| voloshin-hypergraph_FO1430 | 194 | 1.000 | w\left(T_{1}^{\prime}\right) \geq w\left(T_{1}\right)+1 | | |
| voloshin-hypergraph_FO1431 | 194 | 1.000 | \left|\mathcal{D}_{T}(x)\right| | | |
| voloshin-hypergraph_FO1432 | 194 | 1.000 | T^{\prime} | | |
| voloshin-hypergraph_FO1433 | 194 | 1.000 | w\left(T_{1}^{\prime}\right)=w\left(T_{1}\right) | | |
| voloshin-hypergraph_FO1434 | 195 | 1.000 | m_{2}=0 | | |
| voloshin-hypergraph_FO1435 | 195 | 1.000 | |\mathcal{D}(x)|=\left|\mathcal{D}_{T}(x)\right| | | |
| voloshin-hypergraph_FO1436 | 195 | 0.919 | \Lambda\left(\mathcal{H}_{1}, T_{1}\right)=\Lambda\left(\mathcal{H}_{1}\right) | | |
| voloshin-hypergraph_FO1437 | 195 | 0.919 | \Lambda(\mathcal{H})=\Lambda\left(\mathcal{H}_{1}\right) | | |
| voloshin-hypergraph_FO1438 | 195 | 0.876 | \wedge(\mathcal{H})=0 | | |
| voloshin-hypergraph_FO1439 | 195 | 1.000 | 1 \Rightarrow 2 | | |
| voloshin-hypergraph_FO1440 | 195 | 0.923 | \Lambda(\mathcal{H}) | | |
| voloshin-hypergraph_FO1441 | 195 | 0.993 | 2 \Rightarrow 3 | | |
| voloshin-hypergraph_FO1442 | 195 | 1.000 | 3 \Rightarrow 1 | | |
| voloshin-hypergraph_FO1443 | 195 | 0.914 | \wedge(\mathcal{H}) | | |
| voloshin-hypergraph_FO1444 | 196 | 1.000 | w(\mathcal{H}) | | |
| voloshin-hypergraph_FO1445 | 196 | 0.666 | \Lambda(\mathcal{H})=\sum_{D \in \mathcal{D}}(|D|-1)-w(\mathcal{H}) | | |
| voloshin-hypergraph_FO1446 | 197 | 0.999 | D_{0}, D_{1}, D_{2}, \ldots D_{t-1} | | |
| voloshin-hypergraph_FO1447 | 198 | 0.408 | \tau\left(\mathcal{H}^{\prime}\right)=v\left(\mathcal{H}^{\prime}\right) | | |
| voloshin-hypergraph_FO1448 | 198 | 0.408 | v\left(\mathcal{H}^{\prime}\right)=1 | | |
| voloshin-hypergraph_FO1449 | 198 | 0.999 | \tau\left(\mathcal{H}^{\prime}\right)=1 | | |
| voloshin-hypergraph_FO1450 | 198 | 1.000 | >3 | | |
| voloshin-hypergraph_FO1451 | 199 | 0.999 | K_{n},, K_{m, n}, W_{n} | | |
| voloshin-hypergraph_FO1452 | 200 | 1.000 | C_{n}, n \geq 3 | | |
| voloshin-hypergraph_FO1453 | 201 | 1.000 | \chi^{\prime}(\mathcal{H}) | | |
| voloshin-hypergraph_FO1454 | 201 | 1.000 | \chi^{\prime}(\mathcal{H})=\chi(L(\mathcal{H})) | | |
| voloshin-hypergraph_FO1455 | 201 | 1.000 | \chi^{\prime}(\mathcal{H})=\Delta(\mathcal{H}) | | |
| voloshin-hypergraph_FO1456 | 201 | 0.996 | \chi\left(\left(\mathcal{H}^{*}\right)_{2}\right)= | | |
| voloshin-hypergraph_FO1457 | 201 | 1.000 | \omega\left(\left(\mathcal{H}^{*}\right)_{2}\right) | | |
| voloshin-hypergraph_FO1458 | 201 | 0.992 | \tau\left(\mathcal{H}^{\prime}\right)=\mathcal{V}\left(\mathcal{H}^{\prime}\right)=1 | | |
| voloshin-hypergraph_FO1459 | 201 | 0.998 | \chi^{\prime}(\mathcal{H})=\Delta\left(\mathcal{H}^{\prime}\right) | | |
| voloshin-hypergraph_FO1460 | 201 | 0.998 | \chi\left(\left(\mathcal{H}^{*}\right)_{2}\right)=\omega\left(\left(\mathcal{H}^{*}\right)_{2}\right) | | |
| voloshin-hypergraph_FO1461 | 201 | 0.687 | \chi^{\prime}(\mathcal{H})= | | |
| voloshin-hypergraph_FO1462 | 202 | 1.000 | \Delta(\mathcal{H}) | | |
| voloshin-hypergraph_FO1463 | 202 | 1.000 | K_{n}, K_{m, n}, C_{n}, W_{n} | | |
| voloshin-hypergraph_FO1464 | 203 | 1.000 | d \in \mathcal{D} | | |
| voloshin-hypergraph_FO1465 | 204 | 1.000 | f_{2} | | |
| voloshin-hypergraph_FO1466 | 204 | 0.725 | 1,2,3 | | |
| voloshin-hypergraph_FO1467 | 204 | 1.000 | \mathcal{H}=(X, \mathcal{D}),|X|=n,|\mathcal{D}|=m | | |
| voloshin-hypergraph_FO1468 | 204 | 1.000 | n^{\prime}= | | |
| voloshin-hypergraph_FO1469 | 204 | 1.000 | n+m | | |
| voloshin-hypergraph_FO1470 | 205 | 1.000 | f^{\prime}=f | | |
| voloshin-hypergraph_FO1471 | 205 | 1.000 | f_{1}, f_{2}, f_{3}, f_{4}, f_{5} | | |
| voloshin-hypergraph_FO1472 | 205 | 1.000 | f_{6} | | |
| voloshin-hypergraph_FO1473 | 205 | 1.000 | f_{1}, \ldots, f_{6} | | |
| voloshin-hypergraph_FO1474 | 209 | 1.000 | \leq 1 | | |
| voloshin-hypergraph_FO1475 | 209 | 1.000 | \chi(\mathcal{H}) | | |
| voloshin-hypergraph_FO1476 | 209 | 1.000 | \lambda>n | | |
| voloshin-hypergraph_FO1477 | 209 | 0.703 | S_{1}, S_{2}, \ldots, S_{k} | | |
| voloshin-hypergraph_FO1478 | 209 | 0.703 | S_{i} | | |
| voloshin-hypergraph_FO1479 | 210 | 1.000 | \left|S_{i}\right| \leq \alpha(\mathcal{H}) | | |
| voloshin-hypergraph_FO1480 | 210 | 0.999 | \tau+1 | | |
| voloshin-hypergraph_FO1481 | 210 | 0.824 | \tau+1=n-\alpha+1 | | |
| voloshin-hypergraph_FO1482 | 210 | 1.000 | \tau(\mathcal{H})=2 | | |
| voloshin-hypergraph_FO1483 | 210 | 1.000 | \chi(\mathcal{H})=2 | | |
| voloshin-hypergraph_FO1484 | 210 | 1.000 | \alpha(\mathcal{H}) \chi(\mathcal{H}) \geq n | | |
| voloshin-hypergraph_FO1485 | 210 | 1.000 | 3 \cdot 2 \geq 5 | | |
| voloshin-hypergraph_FO1486 | 210 | 1.000 | \chi(\mathcal{H}) \leq \tau(\mathcal{H})+1 | | |
| voloshin-hypergraph_FO1487 | 210 | 1.000 | 2 \leq 2+1 | | |
| voloshin-hypergraph_FO1488 | 210 | 1.000 | \gamma(\mathcal{H}) | | |
| voloshin-hypergraph_FO1489 | 210 | 0.991 | \gamma(\mathcal{H}) \geq \chi(\mathcal{H}) | | |
| voloshin-hypergraph_FO1490 | 211 | 0.998 | S_{i}, i=1,2, \ldots, \lambda | | |
| voloshin-hypergraph_FO1491 | 211 | 1.000 | \lfloor r\rfloor | | |
| voloshin-hypergraph_FO1492 | 211 | 1.000 | \lceil r\rceil | | |
| voloshin-hypergraph_FO1493 | 211 | 1.000 | i=1,2, \ldots, \lambda | | |
| voloshin-hypergraph_FO1494 | 211 | 1.000 | \lambda \geq \max _{D \in \mathcal{D}}|D| | | |
| voloshin-hypergraph_FO1495 | 211 | 1.000 | \left(S_{1}, S_{2}, \ldots, S_{\lambda}\right) | | |
| voloshin-hypergraph_FO1496 | 211 | 1.000 | a_{j}, b_{j} | | |
| voloshin-hypergraph_FO1497 | 211 | 1.000 | a_{j}=0 | | |
| voloshin-hypergraph_FO1498 | 211 | 1.000 | b_{j}=\max \left\{1,\left|D_{j}\right|-1\right\} | | |
| voloshin-hypergraph_FO1499 | 211 | 1.000 | b_{j}=1 | | |
| voloshin-hypergraph_FO1500 | 211 | 1.000 | a_{j}=\left\lfloor\frac{\left|D_{j}\right|}{\lambda}\right\rfloor | | |
| voloshin-hypergraph_FO1501 | 211 | 1.000 | b_{j}=\left\lceil\frac{\left|D_{j}\right|}{\lambda}\right\rceil | | |
| voloshin-hypergraph_FO1502 | 211 | 0.999 | b_{j}=\left|D_{j}\right| | | |
| voloshin-hypergraph_FO1503 | 211 | 0.998 | \left|S_{i} \cap D_{j}\right| \geq 2 | | |
| voloshin-hypergraph_FO1504 | 212 | 1.000 | T= | | |
| voloshin-hypergraph_FO1505 | 212 | 0.982 | \wedge(\mathcal{H})+2 | | |
| voloshin-hypergraph_FO1506 | 212 | 0.881 | h, k, l | | |
| voloshin-hypergraph_FO1507 | 212 | 0.972 | \chi(\mathcal{H})=k | | |
| voloshin-hypergraph_FO1508 | 212 | 1.000 | <l | | |
| voloshin-hypergraph_FO1509 | 212 | 1.000 | \chi(\mathcal{H})=k, k \geq 3 | | |
| voloshin-hypergraph_FO1510 | 212 | 0.998 | \chi\left(\mathcal{H}^{\prime}\right)=k-1 | | |
| voloshin-hypergraph_FO1511 | 212 | 1.000 | \chi(\mathcal{H}) \geq 3 | | |
| voloshin-hypergraph_FO1512 | 212 | 1.000 | \chi(\mathcal{H})=3 | | |
| voloshin-hypergraph_FO1513 | 212 | 0.727 | \chi(\mathcal{H})>k(\chi(\mathcal{H}) \leq k) | | |
| voloshin-hypergraph_FO1514 | 212 | 0.999 | \alpha(\mathcal{H}), \tau(\mathcal{H}) | | |
| voloshin-hypergraph_FO1515 | 213 | 1.000 | m(x, \mathcal{H}) | | |
| voloshin-hypergraph_FO1516 | 213 | 1.000 | \mathcal{D}_{1}(x) \subseteq \mathcal{D}(x) | | |
| voloshin-hypergraph_FO1517 | 214 | 1.000 | M(\mathcal{H}) | | |
| voloshin-hypergraph_FO1518 | 214 | 0.585 | \boldsymbol{\omega} | | |
| voloshin-hypergraph_FO1519 | 214 | 1.000 | c(x) | | |
| voloshin-hypergraph_FO1520 | 214 | 1.000 | c=\left(c\left(x_{1}\right), c\left(x_{2}\right), \ldots, c\left(x_{n}\right)\right) | | |
| voloshin-hypergraph_FO1521 | 214 | 1.000 | \mathcal{H} ; c(x)=0 | | |
| voloshin-hypergraph_FO1522 | 214 | 1.000 | \mathcal{H}=(X, \mathcal{D}), X=\{1,2, \ldots, n\} | | |
| voloshin-hypergraph_FO1523 | 214 | 1.000 | c=(c(1), c(2), \ldots, c(n)) | | |
| voloshin-hypergraph_FO1524 | 214 | 0.994 | C=(0,0, \ldots, 0), i=n, \mathcal{H}_{n}=\mathcal{H} | | |
| voloshin-hypergraph_FO1525 | 214 | 0.994 | \mathcal{H}_{n} | | |
| voloshin-hypergraph_FO1526 | 214 | 0.998 | i:=i-1 | | |
| voloshin-hypergraph_FO1527 | 214 | 1.000 | \mathcal{H}_{i}=\mathcal{H}_{i+1}-x_{i+1} | | |
| voloshin-hypergraph_FO1528 | 214 | 1.000 | \mathcal{H}_{i} | | |
| voloshin-hypergraph_FO1529 | 214 | 1.000 | c\left(x_{1}\right)=1, i=1 | | |
| voloshin-hypergraph_FO1530 | 214 | 1.000 | i=n+1 | | |
| voloshin-hypergraph_FO1531 | 214 | 0.992 | \{1,2, \ldots, n\} | | |
| voloshin-hypergraph_FO1532 | 215 | 1.000 | t \leq M(\mathcal{H}) | | |
| voloshin-hypergraph_FO1533 | 215 | 1.000 | t \geq M(\mathcal{H}) | | |
| voloshin-hypergraph_FO1534 | 215 | 0.973 | y \in Y | | |
| voloshin-hypergraph_FO1535 | 215 | 1.000 | \mathcal{H}_{k} | | |
| voloshin-hypergraph_FO1536 | 215 | 1.000 | t=M(\mathcal{H}) | | |
| voloshin-hypergraph_FO1537 | 215 | 1.000 | 1,2, \ldots, t | | |
| voloshin-hypergraph_FO1538 | 215 | 0.972 | D_{1}, D_{2}, \ldots, D_{t} | | |
| voloshin-hypergraph_FO1539 | 215 | 1.000 | \mathcal{H}_{5}=\mathcal{H} | | |
| voloshin-hypergraph_FO1540 | 215 | 1.000 | X=\{1,2,3,4,5\} | | |
| voloshin-hypergraph_FO1541 | 216 | 1.000 | \min \{2,2,2,1,1\}=1 | | |
| voloshin-hypergraph_FO1542 | 216 | 0.774 | \mathcal{H}_{4}=\mathcal{H}_{5}-5 | | |
| voloshin-hypergraph_FO1543 | 216 | 1.000 | \mathcal{H}_{5}, \mathcal{H}_{4}, \mathcal{H}_{3}, \mathcal{H}_{2} | | |
| voloshin-hypergraph_FO1544 | 216 | 1.000 | \mathcal{H}_{1}=(\{2\}, \emptyset) | | |
| voloshin-hypergraph_FO1545 | 217 | 1.000 | M(\mathcal{H})=2 | | |
| voloshin-hypergraph_FO1546 | 217 | 1.000 | \chi(\mathcal{H})=2 \leq M(\mathcal{H})+1=3 | | |
| voloshin-hypergraph_FO1547 | 218 | 1.000 | X=\left\{x_{1}, x_{2}, \ldots, x_{n}\right\}, n \geq 1 | | |
| voloshin-hypergraph_FO1548 | 218 | 1.000 | \mathcal{C}=\left\{C_{1}, C_{2}, \ldots, C_{l}\right\} | | |
| voloshin-hypergraph_FO1549 | 218 | 1.000 | \mathcal{D}= | | |
| voloshin-hypergraph_FO1550 | 218 | 1.000 | \left\{D_{1}, D_{2}, \ldots, D_{m}\right\} | | |
| voloshin-hypergraph_FO1551 | 218 | 1.000 | \mathcal{C} \cup \mathcal{D} | | |
| voloshin-hypergraph_FO1552 | 218 | 1.000 | \mathcal{C}, \mathcal{D} | | |
| voloshin-hypergraph_FO1553 | 218 | 0.224 | \mathcal{C} \neq \boldsymbol{\emptyset} | | |
| voloshin-hypergraph_FO1554 | 218 | 0.224 | I=\{1,2, \ldots, l\} | | |
| voloshin-hypergraph_FO1555 | 218 | 0.224 | \mathcal{D} \neq \emptyset | | |
| voloshin-hypergraph_FO1556 | 218 | 1.000 | J=\{1,2, \ldots, m\} | | |
| voloshin-hypergraph_FO1557 | 218 | 0.993 | \mathcal{H}=(X, \mathcal{C}, \mathcal{D}) | | |
| voloshin-hypergraph_FO1558 | 218 | 1.000 | V(\mathcal{H}), \mathcal{C} | | |
| voloshin-hypergraph_FO1559 | 218 | 1.000 | \mathcal{C}(\mathcal{H}) | | |
| voloshin-hypergraph_FO1560 | 218 | 1.000 | c(x), x \in X | | |
| voloshin-hypergraph_FO1561 | 218 | 0.833 | \mathcal{H}=(X, C, \mathcal{D}) | | |
| voloshin-hypergraph_FO1562 | 218 | 1.000 | c: X \rightarrow\{1,2, \ldots, \lambda\} | | |
| voloshin-hypergraph_FO1563 | 218 | 0.952 | \mathcal{C}=\emptyset | | |
| voloshin-hypergraph_FO1564 | 218 | 1.000 | X=\{1,2\}, \mathcal{C}=\{\{1,2\}\} | | |
| voloshin-hypergraph_FO1565 | 218 | 1.000 | \mathcal{D}=\{\{1,2\}\} | | |
| voloshin-hypergraph_FO1566 | 218 | 0.848 | C=\{1,2\} | | |
| voloshin-hypergraph_FO1567 | 218 | 1.000 | D=\{1,2\} | | |
| voloshin-hypergraph_FO1568 | 219 | 0.999 | c_{1}, c_{2} | | |
| voloshin-hypergraph_FO1569 | 219 | 1.000 | c_{1}(x) \neq c_{2}(x) | | |
| voloshin-hypergraph_FO1570 | 219 | 1.000 | P(\mathcal{H}, \lambda) | | |
| voloshin-hypergraph_FO1571 | 219 | 1.000 | 1 \leq i \leq n | | |
| voloshin-hypergraph_FO1572 | 219 | 1.000 | \bar{\chi}(\mathcal{H}) | | |
| voloshin-hypergraph_FO1573 | 219 | 1.000 | c(y), y \in Y | | |
| voloshin-hypergraph_FO1574 | 219 | 0.991 | \ldots, X_{i} | | |
| voloshin-hypergraph_FO1575 | 219 | 1.000 | c=X_{1} \cup X_{2} \cup \ldots \cup X_{i} | | |
| voloshin-hypergraph_FO1576 | 219 | 1.000 | r_{i}(\mathcal{H})=r_{i}, 1 \leq i \leq n | | |
| voloshin-hypergraph_FO1577 | 220 | 0.693 | \mathcal{X} | | |
| voloshin-hypergraph_FO1578 | 220 | 0.998 | \bar{\chi} | | |
| voloshin-hypergraph_FO1579 | 220 | 0.924 | r_{i} i! | | |
| voloshin-hypergraph_FO1580 | 220 | 0.924 | \lambda \geq i | | |
| voloshin-hypergraph_FO1581 | 220 | 1.000 | \binom{\lambda}{i} | | |
| voloshin-hypergraph_FO1582 | 220 | 0.993 | \binom{\lambda}{i} r_{i} i!=r_{i} \lambda(\lambda-1) \ldots(\lambda-i+1)= | | |
| voloshin-hypergraph_FO1583 | 220 | 0.998 | r_{i} \lambda^{(i)} | | |
| voloshin-hypergraph_FO1584 | 220 | 0.907 | \chi(\mathcal{H}) \leq i \leq \bar{\chi}(\mathcal{H}) | | |
| voloshin-hypergraph_FO1585 | 220 | 0.968 | r_{\bar{\chi}} | | |
| voloshin-hypergraph_FO1586 | 220 | 1.000 | \mathcal{H}=(X, \mathcal{C}, \emptyset) | | |
| voloshin-hypergraph_FO1587 | 220 | 0.996 | \mathcal{H}_{\mathcal{C}}=(X, \mathcal{C}) | | |
| voloshin-hypergraph_FO1588 | 220 | 1.000 | \mathcal{H}=(X, \emptyset, \mathcal{D}) | | |
| voloshin-hypergraph_FO1589 | 220 | 1.000 | \mathcal{H}_{\mathcal{D}}=(X, \mathcal{D}) | | |
| voloshin-hypergraph_FO1590 | 220 | 0.699 | \mathcal{H}_{\mathcal{C}} | | |
| voloshin-hypergraph_FO1591 | 220 | 0.699 | \mathcal{H}_{\mathcal{D}} | | |
| voloshin-hypergraph_FO1592 | 221 | 0.942 | \bar{\chi}\left(\mathcal{H}_{\mathcal{C}}\right) | | |
| voloshin-hypergraph_FO1593 | 221 | 0.997 | \mathcal{H}_{C} | | |
| voloshin-hypergraph_FO1594 | 221 | 0.742 | \chi\left(\mathcal{H}_{\mathcal{C}}\right)=1, r_{1}\left(\mathcal{H}_{\mathcal{C}}\right)=1 | | |
| voloshin-hypergraph_FO1595 | 221 | 0.742 | \bar{\chi}\left(\mathcal{H}_{\mathcal{D}}\right)=n(\mathcal{H}), r_{n}\left(\mathcal{H}_{\mathcal{D}}\right)=1 | | |
| voloshin-hypergraph_FO1602 | 222 | 0.808 | \bar{\chi}\left(\mathcal{H}_{\mathcal{C}}\right)<\chi\left(\mathcal{H}_{\mathcal{D}}\right) | | |
| voloshin-hypergraph_FO1603 | 222 | 1.000 | \{1,3,4\} | | |
| voloshin-hypergraph_FO1604 | 222 | 1.000 | \mathcal{C}=\mathcal{D} | | |
| voloshin-hypergraph_FO1605 | 222 | 0.806 | \mathcal{E}=\mathcal{C} \cup \mathcal{D} | | |
| voloshin-hypergraph_FO1606 | 222 | 0.994 | \mathcal{H}^{\prime}=(X, \mathcal{E}) | | |
| voloshin-hypergraph_FO1607 | 222 | 0.907 | \mathcal{H}_{C}\left(\mathcal{H}_{\mathcal{D}}\right) | | |
| voloshin-hypergraph_FO1608 | 222 | 1.000 | \mathcal{H}_{Y}=\left(Y, \mathcal{C}^{\prime}, \mathcal{D}^{\prime}\right) | | |
| voloshin-hypergraph_FO1609 | 222 | 1.000 | \mathcal{C}^{\prime} | | |
| voloshin-hypergraph_FO1610 | 222 | 1.000 | R(\mathcal{H}) | | |
| voloshin-hypergraph_FO1611 | 223 | 1.000 | \mathcal{H}=(X, \mathcal{C}) | | |
| voloshin-hypergraph_FO1612 | 223 | 1.000 | \mathcal{C}(x) | | |
| voloshin-hypergraph_FO1613 | 223 | 0.639 | \mathcal{C}(x) \bigcap \mathcal{C}(y) \neq \emptyset | | |
| voloshin-hypergraph_FO1614 | 223 | 0.639 | \mathcal{C}(x) \cap \mathcal{C}(y) | | |
| voloshin-hypergraph_FO1615 | 224 | 1.000 | o(x, \mathcal{H})=0 | | |
| voloshin-hypergraph_FO1616 | 224 | 0.997 | |\mathcal{C}(x)|-1 | | |
| voloshin-hypergraph_FO1617 | 224 | 1.000 | O(\mathcal{H}) | | |
| voloshin-hypergraph_FO1618 | 224 | 0.988 | M \subseteq X | | |
| voloshin-hypergraph_FO1619 | 224 | 1.000 | x \in M | | |
| voloshin-hypergraph_FO1620 | 224 | 1.000 | M C(x) | | |
| voloshin-hypergraph_FO1621 | 224 | 0.783 | M | | |
| voloshin-hypergraph_FO1622 | 224 | 1.000 | \mathcal{H}=(X, \mathcal{C}),|X|=n | | |
| voloshin-hypergraph_FO1623 | 224 | 1.000 | i=n, \mathcal{H}_{n}=\mathcal{H} | | |
| voloshin-hypergraph_FO1624 | 225 | 0.706 | U=\{1\} | | |
| voloshin-hypergraph_FO1625 | 225 | 0.706 | i= | | |
| voloshin-hypergraph_FO1626 | 225 | 0.999 | i=n | | |
| voloshin-hypergraph_FO1627 | 225 | 1.000 | U:=U \cup\{ | | |
| voloshin-hypergraph_FO1628 | 225 | 1.000 | \} | | |
| voloshin-hypergraph_FO1629 | 225 | 1.000 | := | | |
| voloshin-hypergraph_FO1630 | 225 | 0.758 | U:=U-\{ | | |
| voloshin-hypergraph_FO1631 | 225 | 0.971 | M C(y) | | |
| voloshin-hypergraph_FO1632 | 225 | 1.000 | U | | |
| voloshin-hypergraph_FO1633 | 225 | 1.000 | |X|=n,|\mathcal{C}|=k | | |
| voloshin-hypergraph_FO1634 | 225 | 1.000 | n \times k | | |
| voloshin-hypergraph_FO1635 | 225 | 1.000 | O(n k) | | |
| voloshin-hypergraph_FO1636 | 225 | 1.000 | O\left(n^{2} k\right) | | |
| voloshin-hypergraph_FO1637 | 225 | 1.000 | O\left(n^{3} k\right) | | |
| voloshin-hypergraph_FO1638 | 225 | 1.000 | X= | | |
| voloshin-hypergraph_FO1639 | 225 | 0.852 | \{1,2,3,4,5\}, C=\left\{C_{1}, C_{2}, C_{3}, C_{4}, C_{5}\right\}, C_{1}=\{1,2,3\}, C_{2}=\{2,3,4\}, C_{3}=\{3,4,5\} | | |
| voloshin-hypergraph_FO1640 | 225 | 1.000 | C_{4}=\{4,5,1\} | | |
| voloshin-hypergraph_FO1641 | 225 | 1.000 | C_{5}=\{5,1,2\} | | |
| voloshin-hypergraph_FO1642 | 225 | 0.669 | x_{5}=1 | | |
| voloshin-hypergraph_FO1643 | 225 | 0.967 | \mathcal{H}_{4}=\left(X_{4}, \mathcal{C}_{4}\right) | | |
| voloshin-hypergraph_FO1644 | 225 | 0.967 | X_{4}=\{2,3,4,5\}, \mathcal{C}_{4}=\left\{C_{2}, C_{3}\right\} | | |
| voloshin-hypergraph_FO1645 | 225 | 1.000 | x_{4}=2 | | |
| voloshin-hypergraph_FO1646 | 225 | 1.000 | \mathcal{H}_{3}=\left(X_{3}, \mathcal{C}_{3}\right) | | |
| voloshin-hypergraph_FO1647 | 225 | 1.000 | X_{3}=\{3,4,5\}, \mathcal{C}_{3}=\left\{C_{3}\right\} | | |
| voloshin-hypergraph_FO1648 | 225 | 1.000 | x_{3}=3 | | |
| voloshin-hypergraph_FO1649 | 225 | 1.000 | \mathcal{H}_{2}=\left(X_{2}, \mathcal{C}_{2}\right) | | |
| voloshin-hypergraph_FO1650 | 225 | 1.000 | X_{2}=\{4,5\}, \mathcal{C}_{2}=\{\emptyset\} | | |
| voloshin-hypergraph_FO1651 | 225 | 1.000 | x_{2}=4 | | |
| voloshin-hypergraph_FO1652 | 226 | 0.984 | \mathcal{H}_{1}=\left(X_{1}, \mathcal{C}_{1}\right) | | |
| voloshin-hypergraph_FO1653 | 226 | 0.984 | X_{1}=\{5\}, \mathcal{C}_{1}=\{\emptyset\} | | |
| voloshin-hypergraph_FO1654 | 226 | 1.000 | x_{1}=5 | | |
| voloshin-hypergraph_FO1655 | 226 | 0.976 | c(i) | | |
| voloshin-hypergraph_FO1656 | 226 | 0.976 | i, c(i)=0 | | |
| voloshin-hypergraph_FO1657 | 226 | 1.000 | i=1, \ldots, 5 | | |
| voloshin-hypergraph_FO1658 | 226 | 1.000 | c=(c(1), c(2), c(3), c(4), c(5))=(0,0,0,0,0) | | |
| voloshin-hypergraph_FO1659 | 226 | 1.000 | c= | | |
| voloshin-hypergraph_FO1660 | 226 | 0.921 | c=(0,0,0,2,1) | | |
| voloshin-hypergraph_FO1661 | 226 | 1.000 | c=(0,0,3,2,1) | | |
| voloshin-hypergraph_FO1662 | 226 | 0.991 | c=(0,0,2,2,1) | | |
| voloshin-hypergraph_FO1663 | 226 | 0.980 | c=(0,3,2,2,1) | | |
| voloshin-hypergraph_FO1664 | 226 | 0.964 | c=(4,3,2,2,1) | | |
| voloshin-hypergraph_FO1665 | 226 | 1.000 | C_{1}, C_{4}, C_{5} | | |
| voloshin-hypergraph_FO1666 | 226 | 1.000 | \mathcal{H}_{5} | | |
| voloshin-hypergraph_FO1667 | 226 | 0.910 | c(5)=1: c=(1,3,2,2,1) | | |
| voloshin-hypergraph_FO1668 | 226 | 1.000 | M C(3)=\{3,4\}: c=(1,3,1,1,1) | | |
| voloshin-hypergraph_FO1669 | 226 | 0.948 | \mathcal{H}_{1}=\mathcal{H} | | |
| voloshin-hypergraph_FO1670 | 227 | 1.000 | c=(1,2,1,1,1) | | |
| voloshin-hypergraph_FO1671 | 227 | 1.000 | C=(4,3,2,2,1) | | |
| voloshin-hypergraph_FO1672 | 227 | 0.982 | 1,2,3,4,5 \ldots | | |
| voloshin-hypergraph_FO1673 | 227 | 0.999 | t \leq O(\mathcal{H}) | | |
| voloshin-hypergraph_FO1674 | 227 | 1.000 | t \leq O(\mathcal{H})-1 | | |
| voloshin-hypergraph_FO1675 | 227 | 1.000 | \geq t+1 | | |
| voloshin-hypergraph_FO1676 | 227 | 1.000 | t=O(\mathcal{H}) | | |
| voloshin-hypergraph_FO1677 | 227 | 1.000 | O(\mathcal{H})+1 | | |
| voloshin-hypergraph_FO1678 | 227 | 1.000 | c(y) | | |
| voloshin-hypergraph_FO1679 | 227 | 0.971 | b\left(x_{i}, \mathcal{H}_{i}\right) \mathcal{C} | | |
| voloshin-hypergraph_FO1680 | 227 | 0.990 | o\left(x_{i}, \mathcal{H}_{i}\right)=\left|\mathcal{C}\left(x_{i}\right)\right|-b\left(x_{i}, \mathcal{H}_{i}\right) \mathcal{C} | | |
| voloshin-hypergraph_FO1681 | 227 | 1.000 | o\left(x_{i}, \mathcal{H}_{i}\right) | | |
| voloshin-hypergraph_FO1682 | 227 | 1.000 | o\left(x_{i}, \mathcal{H}_{i}\right)+1 | | |
| voloshin-hypergraph_FO1683 | 227 | 1.000 | i, 1 \leq i \leq n | | |
| voloshin-hypergraph_FO1684 | 227 | 1.000 | O(\mathcal{H})=0 | | |
| voloshin-hypergraph_FO1685 | 227 | 1.000 | |U|=p | | |
| voloshin-hypergraph_FO1686 | 227 | 1.000 | \bar{\chi}(\mathcal{H}) \geq p | | |
| voloshin-hypergraph_FO1687 | 228 | 1.000 | n=2,3 | | |
| voloshin-hypergraph_FO1688 | 228 | 1.000 | O\left(\mathcal{H}_{Y}\right)=0 | | |
| voloshin-hypergraph_FO1689 | 228 | 1.000 | Y \subset X | | |
| voloshin-hypergraph_FO1690 | 228 | 0.902 | \overline{\mathrm{X}}(\mathcal{H}) | | |
| voloshin-hypergraph_FO1691 | 229 | 0.934 | \mathcal{C} \neq \emptyset | | |
| voloshin-hypergraph_FO1692 | 229 | 0.938 | (X, \mathcal{C}, \mathcal{D}) | | |
| voloshin-hypergraph_FO1693 | 229 | 1.000 | C_{i} \subseteq C_{j} | | |
| voloshin-hypergraph_FO1694 | 229 | 1.000 | P(\mathcal{H}, \lambda)=P\left(\mathcal{H}-C_{j}, \lambda\right), R(\mathcal{H})=R\left(\mathcal{H}-C_{j}\right), i, j \in I | | |
| voloshin-hypergraph_FO1695 | 229 | 1.000 | C_{j} | | |
| voloshin-hypergraph_FO1696 | 229 | 1.000 | D_{i} \subseteq D_{j} | | |
| voloshin-hypergraph_FO1697 | 229 | 1.000 | P(\mathcal{H}, \lambda)=P\left(\mathcal{H}-D_{j}, \lambda\right), R(\mathcal{H})=R\left(\mathcal{H}-D_{j}\right), i, j \in J | | |
| voloshin-hypergraph_FO1698 | 230 | 1.000 | \left\{x_{k}, x_{l}\right\} \notin \mathcal{D} | | |
| voloshin-hypergraph_FO1699 | 230 | 1.000 | \left\{x_{k}, x_{l}\right\} \notin \mathcal{C} | | |
| voloshin-hypergraph_FO1700 | 230 | 0.931 | x_{l} | | |
| voloshin-hypergraph_FO1701 | 230 | 1.000 | C_{t}=\left\{x_{k}, x_{l}\right\} | | |
| voloshin-hypergraph_FO1702 | 230 | 1.000 | t \in I | | |
| voloshin-hypergraph_FO1703 | 230 | 1.000 | x_{k}, x_{l} \in X | | |
| voloshin-hypergraph_FO1704 | 230 | 1.000 | C_{t} \neq D_{s} | | |
| voloshin-hypergraph_FO1705 | 230 | 1.000 | s \in J | | |
| voloshin-hypergraph_FO1706 | 230 | 0.619 | \mathcal{H}_{1}=\left(X_{1}, \mathcal{C}^{1}, \mathcal{D}^{1}\right), X_{1}=\left(X \backslash\left\{x_{k}, x_{l}\right\}\right) \cup\{y\}, \quad y | | |
| voloshin-hypergraph_FO1707 | 230 | 1.000 | x_{k} \in D_{j} | | |
| voloshin-hypergraph_FO1708 | 230 | 1.000 | x_{l} \in D_{j}, j \in J | | |
| voloshin-hypergraph_FO1709 | 230 | 1.000 | D_{j}^{1}=\left(D_{j} \backslash\left\{x_{k}, x_{l}\right\}\right) \cup\{y\} | | |
| voloshin-hypergraph_FO1710 | 230 | 1.000 | D_{j}^{1}=D_{j} | | |
| voloshin-hypergraph_FO1711 | 230 | 1.000 | x_{k} \in C_{i} | | |
| voloshin-hypergraph_FO1712 | 230 | 1.000 | x_{l} \in C_{i}, i \in I, i \neq t | | |
| voloshin-hypergraph_FO1713 | 230 | 1.000 | C_{i}^{1}=\left(C_{i} \backslash\left\{x_{k}, x_{l}\right\}\right) \cup\{y\} | | |
| voloshin-hypergraph_FO1714 | 230 | 1.000 | C_{i}^{1}=C_{i} | | |
| voloshin-hypergraph_FO1715 | 230 | 1.000 | n(\mathcal{H})=n\left(\mathcal{H}_{1}\right)+1 | | |
| voloshin-hypergraph_FO1716 | 230 | 1.000 | R(\mathcal{H})=R\left(\mathcal{H}_{1}\right) | | |
| voloshin-hypergraph_FO1717 | 230 | 1.000 | r_{i}(\mathcal{H})=r_{i}\left(\mathcal{H}_{1}\right) | | |
| voloshin-hypergraph_FO1718 | 230 | 1.000 | i=1,2, \ldots, n-1 | | |
| voloshin-hypergraph_FO1719 | 230 | 1.000 | r_{n}(\mathcal{H})=0 | | |
| voloshin-hypergraph_FO1720 | 230 | 1.000 | C_{t} | | |
| voloshin-hypergraph_FO1721 | 230 | 0.982 | 1,2, \ldots, n | | |
| voloshin-hypergraph_FO1722 | 231 | 0.998 | L=Z=Y=\emptyset, R(\mathcal{H})=(0,0, \ldots, 0), P(\mathcal{H}, \lambda)=0, \chi(\mathcal{H})=\bar{\chi}(\mathcal{H})=0 | | |
| voloshin-hypergraph_FO1723 | 231 | 0.588 | i=1,2, \ldots, n | | |
| voloshin-hypergraph_FO1724 | 231 | 1.000 | \chi(\mathcal{H}), \bar{\chi}(\mathcal{H}) | | |
| voloshin-hypergraph_FO1725 | 231 | 0.988 | X=\{1,2 | | |
| voloshin-hypergraph_FO1726 | 231 | 0.698 | 3,4\}, \mathcal{C}=\{C\}=\{\{1,2,3,4\}\}, \mathcal{D}=\left\{D_{1}, D_{2}, D_{3}, D_{4}\right\}=\{\{1,2\},\{2,3\},\{3,4\},\{4,1\}\} | | |
| voloshin-hypergraph_FO1727 | 231 | 1.000 | \chi=2, \bar{\chi}=3 | | |
| voloshin-hypergraph_FO1728 | 231 | 0.999 | (c(1), c(2), c(3), c(4)) | | |
| voloshin-hypergraph_FO1729 | 233 | 1.000 | X=\{1,2,3,4,5\}, \quad \mathcal{C}=\{\{1,2,3\},\{1,3,4\} | | |
| voloshin-hypergraph_FO1730 | 233 | 0.997 | \{1,4,5\},\{1,5,2\}\}, \quad \mathcal{D}=\{\{3,5\}\} | | |
| voloshin-hypergraph_FO1731 | 233 | 0.997 | \bar{\chi}(\mathcal{H})=3 | | |
| voloshin-hypergraph_FO1732 | 233 | 0.967 | \{2,4\} | | |
| voloshin-hypergraph_FO1733 | 233 | 0.967 | \bar{\chi}\left(\mathcal{H}_{1}\right)=2 | | |
| voloshin-hypergraph_FO1734 | 233 | 0.989 | C \in \mathcal{C}(\mathcal{D} | | |
| voloshin-hypergraph_FO1735 | 233 | 1.000 | X=\{1,2,3,4\} | | |
| voloshin-hypergraph_FO1736 | 233 | 1.000 | \mathcal{C}=\{\{1,2,3\} | | |
| voloshin-hypergraph_FO1737 | 233 | 0.987 | \{1,3,4\},\{1,2,4\},\{2,3,4\}\} | | |
| voloshin-hypergraph_FO1738 | 233 | 1.000 | \mathcal{H}^{\prime}=(X, \mathcal{C}, \mathcal{D}) | | |
| voloshin-hypergraph_FO1739 | 233 | 1.000 | \mathcal{H}_{1}, \mathcal{H}_{2}, \ldots, \mathcal{H}_{k} k \geq 2 | | |
| voloshin-hypergraph_FO1740 | 235 | 1.000 | \mathcal{H}_{1}=\left(\{1,2,3,4\}, K_{4}^{3}, \emptyset\right) | | |
| voloshin-hypergraph_FO1741 | 235 | 1.000 | \mathcal{H}_{2}= | | |
| voloshin-hypergraph_FO1742 | 235 | 0.957 | \left(\{1,2,3,4\}, \emptyset, K_{4}^{3}\right) | | |
| voloshin-hypergraph_FO1743 | 235 | 1.000 | \mathcal{D}=\left\{D_{1}, D_{2}\right. | | |
| voloshin-hypergraph_FO1744 | 235 | 0.999 | \left.\ldots, D_{m}\right\} | | |
| voloshin-hypergraph_FO1745 | 235 | 0.999 | J= | | |
| voloshin-hypergraph_FO1746 | 235 | 1.000 | \{1,2, \ldots, m\} | | |
| voloshin-hypergraph_FO1747 | 236 | 1.000 | K_{n}^{k+1} | | |
| voloshin-hypergraph_FO1748 | 236 | 1.000 | \mathcal{H}^{\prime}=\left(X,\binom{X}{k+1}, \mathcal{D}\right) | | |
| voloshin-hypergraph_FO1749 | 236 | 1.000 | \left\{x_{1}, x_{2}\right\} | | |
| voloshin-hypergraph_FO1750 | 236 | 1.000 | v(k) | | |
| voloshin-hypergraph_FO1751 | 236 | 1.000 | \mathcal{H}=(X, \mathcal{C}, \mathcal{D}),|X|=n | | |
| voloshin-hypergraph_FO1752 | 236 | 1.000 | \bar{\chi}\left(\mathcal{H}_{\mathcal{C}}\right)-\chi\left(\mathcal{H}_{\mathcal{D}}\right)=k | | |
| voloshin-hypergraph_FO1753 | 236 | 0.816 | k=0,1,2, \ldots | | |
| voloshin-hypergraph_FO1754 | 236 | 0.554 | \bar{\chi}\left(\mathcal{H}_{C}\right)-\chi\left(\mathcal{H}_{\mathcal{D}}\right) | | |
| voloshin-hypergraph_FO1755 | 236 | 0.996 | n-2=k+1 | | |
| voloshin-hypergraph_FO1757 | 237 | 1.000 | n=|X| \geq 2 | | |
| voloshin-hypergraph_FO1758 | 237 | 0.836 | \mathcal{U}_{n}=\left(X,\binom{X}{2},\binom{X}{2}\right. | | |
| voloshin-hypergraph_FO1759 | 237 | 0.910 | \mathcal{U}_{n} | | |
| voloshin-hypergraph_FO1760 | 237 | 0.706 | \mathcal{U}{ }_{4} | | |
| voloshin-hypergraph_FO1761 | 237 | 0.906 | |X|=n=v(k) | | |
| voloshin-hypergraph_FO1762 | 237 | 0.906 | n=v(k)=k+4 | | |
| voloshin-hypergraph_FO1763 | 237 | 1.000 | n \geq k+4 | | |
| voloshin-hypergraph_FO1764 | 237 | 1.000 | n<k+4 | | |
| voloshin-hypergraph_FO1765 | 237 | 0.959 | \chi\left(\mathcal{H}_{\mathcal{D}}\right) \geq 2 | | |
| voloshin-hypergraph_FO1766 | 237 | 0.959 | \chi\left(\mathcal{H}_{\mathcal{D}}\right) \geq 3 | | |
| voloshin-hypergraph_FO1767 | 237 | 0.959 | \bar{\chi}\left(\mathcal{H}_{\mathcal{C}}\right) \geq k+3 | | |
| voloshin-hypergraph_FO1768 | 237 | 0.959 | n=k+3 | | |
| voloshin-hypergraph_FO1769 | 237 | 0.984 | \chi\left(\mathcal{H}_{\mathcal{C}}\right)=n | | |
| voloshin-hypergraph_FO1770 | 237 | 0.999 | \chi\left(\mathcal{H}_{\mathcal{D}}\right)=2 | | |
| voloshin-hypergraph_FO1771 | 237 | 1.000 | n=k+2 | | |
| voloshin-hypergraph_FO1772 | 237 | 0.983 | \bar{\chi}\left(\mathcal{H}_{C}\right)=k+2 | | |
| voloshin-hypergraph_FO1773 | 237 | 0.715 | \bar{\chi}\left(\mathcal{H}_{\mathcal{C}}\right)=k+2=n-1 | | |
| voloshin-hypergraph_FO1774 | 237 | 0.715 | \mathcal{H}_{\mathcal{C}}= | | |
| voloshin-hypergraph_FO1775 | 237 | 0.994 | (X, \mathcal{C}) | | |
| voloshin-hypergraph_FO1776 | 239 | 0.743 | k=3 | | |
| voloshin-hypergraph_FO1777 | 238 | 1.000 | v(k)= | | |
| voloshin-hypergraph_FO1778 | 238 | 0.999 | v(k) \leq k+4 | | |
| voloshin-hypergraph_FO1779 | 238 | 0.373 | \bar{\chi}\left(\mathcal{H}_{C}\right)-\chi\left(\mathcal{H}_{\mathcal{D}}\right)=k | | |
| voloshin-hypergraph_FO1780 | 238 | 0.373 | n= | | |
| voloshin-hypergraph_FO1781 | 238 | 1.000 | k+4, k=0,1,2, \ldots | | |
| voloshin-hypergraph_FO1782 | 238 | 1.000 | k=0,1 | | |
| voloshin-hypergraph_FO1783 | 238 | 1.000 | k=0 | | |
| voloshin-hypergraph_FO1784 | 238 | 1.000 | X=\{1,2,3,4\}, \mathcal{C}=\{\{1,2,3\},\{1,2,4\}\}, \mathcal{D}=\{\{1,2\} | | |
| voloshin-hypergraph_FO1785 | 238 | 0.665 | \{2,3\},\{2,4\},\{3,4\}\} | | |
| voloshin-hypergraph_FO1786 | 238 | 1.000 | X=\{1,2,3,4,5\}, \mathcal{C}=\{\{1,2,3\},\{1,2,4\},\{1,2,5\}\} | | |
| voloshin-hypergraph_FO1787 | 238 | 0.950 | \mathcal{D}=\{\{1,2\},\{3,4\},\{4,5\},\{3,5\}\} | | |
| voloshin-hypergraph_FO1788 | 238 | 1.000 | k=2 l, l \geq 1 | | |
| voloshin-hypergraph_FO1789 | 238 | 0.999 | X=\{1,2,3, \ldots, k+4\}, \mathcal{C}= | | |
| voloshin-hypergraph_FO1790 | 238 | 0.990 | \{\{1,2, i\}: 3 \leq i \leq k+4\} | | |
| voloshin-hypergraph_FO1791 | 238 | 0.990 | \mathcal{D}=\{\{i, i+1\}: 1 \leq i \leq k+3\} \cup\{k+4,2\} | | |
| voloshin-hypergraph_FO1792 | 238 | 0.860 | \bar{\chi}\left(\mathcal{H}_{\mathcal{C}}\right)=n-1=k+3 | | |
| voloshin-hypergraph_FO1793 | 238 | 0.990 | (2,3,4, \ldots, k+4,2) | | |
| voloshin-hypergraph_FO1794 | 238 | 0.990 | \chi\left(\mathcal{H}_{\mathcal{D}}\right)=3 | | |
| voloshin-hypergraph_FO1795 | 239 | 0.999 | i, i=1,2, \ldots, n | | |
| voloshin-hypergraph_FO1796 | 239 | 0.998 | c(1)=1, c(2)=2 | | |
| voloshin-hypergraph_FO1797 | 239 | 0.998 | c(3) \neq c(2) | | |
| voloshin-hypergraph_FO1798 | 239 | 0.600 | c(3)= | | |
| voloshin-hypergraph_FO1799 | 239 | 0.993 | c(1)=1 | | |
| voloshin-hypergraph_FO1800 | 239 | 0.993 | c(4) \neq c(3) | | |
| voloshin-hypergraph_FO1801 | 239 | 0.993 | \{1,2,4\} | | |
| voloshin-hypergraph_FO1802 | 239 | 1.000 | c(4)=c(2)=2 | | |
| voloshin-hypergraph_FO1803 | 239 | 0.996 | (2,3,4, \ldots, k+4) | | |
| voloshin-hypergraph_FO1804 | 239 | 1.000 | c(k+3)=1 | | |
| voloshin-hypergraph_FO1805 | 239 | 1.000 | c(2)=2 | | |
| voloshin-hypergraph_FO1806 | 239 | 1.000 | k+4 | | |
| voloshin-hypergraph_FO1807 | 239 | 0.994 | c(k+4) | | |
| voloshin-hypergraph_FO1808 | 239 | 0.994 | \{1,2, k+4\} | | |
| voloshin-hypergraph_FO1809 | 239 | 1.000 | k=2 l+1, l \geq 1 | | |
| voloshin-hypergraph_FO1810 | 239 | 0.936 | \mathcal{D}=\{1,2\} \cup\{\{i, i+1\}: 3 \leq i \leq k+3\} \cup\{k+4,3\} | | |
| voloshin-hypergraph_FO1811 | 239 | 0.929 | (3,4, \ldots, k+4,3) | | |
| voloshin-hypergraph_FO1812 | 239 | 1.000 | c(3) | | |
| voloshin-hypergraph_FO1813 | 239 | 1.000 | c(3)=1 | | |
| voloshin-hypergraph_FO1814 | 239 | 1.000 | c(3)=2 | | |
| voloshin-hypergraph_FO1815 | 239 | 1.000 | c(4)=2, c(5)=1, c(6)=2 | | |
| voloshin-hypergraph_FO1816 | 239 | 1.000 | \{k+3, k+4\} | | |
| voloshin-hypergraph_FO1817 | 239 | 1.000 | \{k+4,3\} | | |
| voloshin-hypergraph_FO1818 | 239 | 1.000 | 2 \leq l, m \leq n=|X| | | |
| voloshin-hypergraph_FO1819 | 239 | 0.996 | |\mathcal{C}|=\binom{n}{l} | | |
| voloshin-hypergraph_FO1820 | 239 | 0.996 | |\mathcal{D}|=\binom{n}{m} | | |
| voloshin-hypergraph_FO1821 | 239 | 0.996 | \mathcal{K}(n, l, m) | | |
| voloshin-hypergraph_FO1822 | 239 | 0.996 | (l, m) | | |
| voloshin-hypergraph_FO1823 | 239 | 1.000 | n, l, m | | |
| voloshin-hypergraph_FO1824 | 239 | 0.740 | \mathcal{K}(4,4,2) | | |
| voloshin-hypergraph_FO1825 | 240 | 1.000 | n \leq(l-1)(m-1) | | |
| voloshin-hypergraph_FO1826 | 240 | 1.000 | m-1 | | |
| voloshin-hypergraph_FO1827 | 240 | 0.994 | l-1 | | |
| voloshin-hypergraph_FO1828 | 240 | 0.998 | n \geq(l-1)(m-1)+1 | | |
| voloshin-hypergraph_FO1829 | 240 | 0.998 | (l-1)(m-1)) | | |
| voloshin-hypergraph_FO1830 | 240 | 1.000 | n+1 | | |
| voloshin-hypergraph_FO1831 | 240 | 1.000 | l=1 | | |
| voloshin-hypergraph_FO1832 | 240 | 1.000 | m=1 | | |
| voloshin-hypergraph_FO1833 | 240 | 1.000 | n^{2} | | |
| voloshin-hypergraph_FO1834 | 240 | 1.000 | 2 \leq l \leq n+1,2 \leq m \leq n+1 | | |
| voloshin-hypergraph_FO1835 | 240 | 1.000 | \mathcal{K}(n, l, m+1) | | |
| voloshin-hypergraph_FO1836 | 240 | 0.997 | l \geq 2 | | |
| voloshin-hypergraph_FO1837 | 240 | 0.997 | \left\lfloor\frac{n}{l-1}\right\rfloor | | |
| voloshin-hypergraph_FO1838 | 240 | 1.000 | N_{n} | | |
| voloshin-hypergraph_FO1840 | 241 | 1.000 | \mathcal{K}(8, l, m) | | |
| voloshin-hypergraph_FO1841 | 241 | 0.926 | l, m | | |
| voloshin-hypergraph_FO1842 | 241 | 0.999 | x, y \in D | | |
| voloshin-hypergraph_FO1843 | 242 | 1.000 | \chi(\mathcal{H}) \leq 2 | | |
| voloshin-hypergraph_FO1844 | 243 | 0.996 | \mathcal{U C} | | |
| voloshin-hypergraph_FO1845 | 243 | 1.000 | r=2 | | |
| voloshin-hypergraph_FO1846 | 244 | 0.712 | x= | | |
| voloshin-hypergraph_FO1847 | 244 | 0.977 | x_{0}, x_{1}, \ldots, x_{k}=y, k \geq 1 | | |
| voloshin-hypergraph_FO1848 | 244 | 0.977 | x_{i} \neq x_{i+1} | | |
| voloshin-hypergraph_FO1849 | 244 | 0.977 | \left(x_{i}, x_{i+1}\right) \in \mathcal{D} | | |
| voloshin-hypergraph_FO1850 | 244 | 1.000 | x_{1}, \ldots, x_{k-1} | | |
| voloshin-hypergraph_FO1851 | 244 | 0.999 | x_{0}, x_{1} | | |
| voloshin-hypergraph_FO1852 | 244 | 1.000 | x_{2}, x_{3} | | |
| voloshin-hypergraph_FO1853 | 244 | 1.000 | x_{0}, x_{1}, x_{2}, x_{3}, x_{4} | | |
| voloshin-hypergraph_FO1854 | 244 | 1.000 | \left(x_{0}, x_{4}\right) | | |
| voloshin-hypergraph_FO1855 | 244 | 0.979 | \chi=\bar{\chi}=2 | | |
| voloshin-hypergraph_FO1856 | 245 | 0.835 | c=X_{1} \cup \cdots \cup X_{t} | | |
| voloshin-hypergraph_FO1857 | 245 | 0.999 | \mathcal{H}^{\prime}=\left(X^{\prime}, \mathcal{C}^{\prime}, \mathcal{D}^{\prime}\right) | | |
| voloshin-hypergraph_FO1858 | 245 | 0.999 | \chi\left(\mathcal{H}^{\prime}\right)=\bar{\chi}\left(\mathcal{H}^{\prime}\right)=t | | |
| voloshin-hypergraph_FO1859 | 245 | 1.000 | T_{i} | | |
| voloshin-hypergraph_FO1860 | 245 | 0.737 | \left\{x=x_{1}, x_{2}, z\right\} | | |
| voloshin-hypergraph_FO1861 | 245 | 1.000 | X_{j} | | |
| voloshin-hypergraph_FO1862 | 245 | 0.591 | x_{i} \in X_{i} | | |
| voloshin-hypergraph_FO1863 | 245 | 0.591 | x_{j} \in X_{j} | | |
| voloshin-hypergraph_FO1864 | 246 | 1.000 | \mu=\left(z_{0}, z_{1}, \ldots, z_{k}=z_{0}\right), k \geq 6 | | |
| voloshin-hypergraph_FO1865 | 246 | 0.983 | z_{0} \neq z_{1} \neq z_{2} \neq z_{0} | | |
| voloshin-hypergraph_FO1866 | 246 | 1.000 | z_{0} \neq z_{2} \neq \ldots \neq z_{k-2} | | |
| voloshin-hypergraph_FO1867 | 246 | 1.000 | z_{1}=z_{3}=\ldots=z_{k-1}=y | | |
| voloshin-hypergraph_FO1868 | 246 | 0.907 | |\mathcal{D}| \leq n-2 | | |
| voloshin-hypergraph_FO1869 | 246 | 1.000 | r_{2}(\mathcal{H}) \geq 2 | | |
| voloshin-hypergraph_FO1870 | 246 | 1.000 | T=(X, \mathcal{E}) | | |
| voloshin-hypergraph_FO1871 | 246 | 1.000 | e=\{x, y\} \notin \mathcal{D} | | |
| voloshin-hypergraph_FO1872 | 246 | 1.000 | c(x)=c(y)=1 | | |
| voloshin-hypergraph_FO1873 | 246 | 0.941 | 2,1,2, \ldots | | |
| voloshin-hypergraph_FO1874 | 246 | 0.941 | c(x)=1 | | |
| voloshin-hypergraph_FO1875 | 246 | 0.941 | c(y)=2 | | |
| voloshin-hypergraph_FO1876 | 246 | 0.982 | u, v \in X | | |
| voloshin-hypergraph_FO1877 | 246 | 0.982 | (u, v) | | |
| voloshin-hypergraph_FO1878 | 246 | 1.000 | u=x_{1}, x_{2}, \ldots, x_{p}=v | | |
| voloshin-hypergraph_FO1879 | 246 | 1.000 | x_{j}, x_{j+1}, x_{j+2} | | |
| voloshin-hypergraph_FO1880 | 246 | 1.000 | \left\{x_{j}, x_{j+1}, x_{j+2}\right\} \notin \mathcal{C} | | |
| voloshin-hypergraph_FO1881 | 246 | 1.000 | x_{j+1} | | |
| voloshin-hypergraph_FO1882 | 246 | 1.000 | c\left(x_{j}\right)=c\left(x_{j+2}\right) | | |
| voloshin-hypergraph_FO1883 | 246 | 0.658 | x_{j+2} | | |
| voloshin-hypergraph_FO1884 | 246 | 1.000 | c\left(x_{j}\right) \neq c\left(x_{j+2}\right) | | |
| voloshin-hypergraph_FO1885 | 246 | 1.000 | \left\{x_{j}, x_{j+1}\right\},\left\{x_{j+1}, x_{j+2}\right\} \in \mathcal{D}, c\left(x_{j}\right) \neq c\left(x_{j+1}\right) \neq c\left(x_{j+2}\right) | | |
| voloshin-hypergraph_FO1886 | 246 | 1.000 | x^{\prime}, y^{\prime} | | |
| voloshin-hypergraph_FO1887 | 246 | 1.000 | c_{1}\left(x^{\prime}\right)=c_{1}\left(y^{\prime}\right) | | |
| voloshin-hypergraph_FO1888 | 246 | 1.000 | c_{2}\left(x^{\prime}\right) \neq c_{2}\left(y^{\prime}\right) | | |
| voloshin-hypergraph_FO1889 | 246 | 1.000 | \left(x^{\prime}, y^{\prime}\right) | | |
| voloshin-hypergraph_FO1890 | 246 | 0.994 | x^{\prime}=x_{0}, x_{1}, \ldots x_{k}=y^{\prime} | | |
| voloshin-hypergraph_FO1891 | 246 | 1.000 | c\left(x^{\prime}\right)=c\left(y^{\prime}\right) | | |
| voloshin-hypergraph_FO1892 | 246 | 1.000 | c\left(x^{\prime}\right) \neq c\left(y^{\prime}\right) | | |
| voloshin-hypergraph_FO1893 | 246 | 1.000 | \mathcal{D}=\mathcal{E} | | |
| voloshin-hypergraph_FO1894 | 247 | 1.000 | R(\mathcal{H})= | | |
| voloshin-hypergraph_FO1895 | 247 | 1.000 | R(\mathcal{H}-C) | | |
| voloshin-hypergraph_FO1896 | 247 | 0.982 | C=\left\{x_{1}, x_{2}, x_{3}\right\} | | |
| voloshin-hypergraph_FO1897 | 247 | 0.982 | \mathcal{H}^{\prime}=\left(X, \mathcal{C}^{\prime}, \mathcal{D}\right) | | |
| voloshin-hypergraph_FO1898 | 247 | 1.000 | \mathcal{C}^{\prime}=\mathcal{C} \backslash\{C\} | | |
| voloshin-hypergraph_FO1899 | 247 | 0.998 | x_{1}=z_{0}, z_{1}, \ldots, z_{k}=x_{3} | | |
| voloshin-hypergraph_FO1900 | 247 | 0.998 | \left(x_{1}, x_{1}\right) | | |
| voloshin-hypergraph_FO1901 | 247 | 1.000 | x_{1}=z_{0}, z_{1}, \ldots, z_{k}=x_{3}, x_{2}, x_{1} | | |
| voloshin-hypergraph_FO1902 | 247 | 0.999 | \left\{x_{1}, x_{2}, x_{3}\right\}=C | | |
| voloshin-hypergraph_FO1903 | 247 | 0.999 | x_{1}=z_{0}, z_{1}, \ldots, z_{k}=x_{3}=\left(x_{1}, x_{3}\right)^{\prime} | | |
| voloshin-hypergraph_FO1904 | 247 | 0.999 | \left(x_{1}, x_{3}\right)^{\prime} | | |
| voloshin-hypergraph_FO1905 | 247 | 0.999 | \mathcal{H}^{\prime}=(X, \mathcal{C} \backslash | | |
| voloshin-hypergraph_FO1906 | 247 | 0.886 | \{C\}, \mathcal{D}) | | |
| voloshin-hypergraph_FO1907 | 247 | 1.000 | X=X_{1} \cup X_{2} \cup \ldots \cup X_{i} | | |
| voloshin-hypergraph_FO1908 | 247 | 0.913 | \mathcal{H}, \chi(\mathcal{H}) \leq i \leq \bar{\chi}(\mathcal{H}) | | |
| voloshin-hypergraph_FO1909 | 247 | 1.000 | L_{j}=\left(X_{j}, E_{j}\right) | | |
| voloshin-hypergraph_FO1910 | 247 | 0.699 | E_{j} | | |
| voloshin-hypergraph_FO1911 | 247 | 0.699 | \{x, y\} \in E_{j} | | |
| voloshin-hypergraph_FO1912 | 247 | 1.000 | C \cap X_{j}=\{x, y\} | | |
| voloshin-hypergraph_FO1913 | 247 | 1.000 | \left|C \cap X_{k}\right| \leq 1 | | |
| voloshin-hypergraph_FO1914 | 247 | 1.000 | k \neq j | | |
| voloshin-hypergraph_FO1915 | 247 | 0.998 | \bar{\chi}+1 | | |
| voloshin-hypergraph_FO1916 | 247 | 1.000 | L_{1} | | |
| voloshin-hypergraph_FO1917 | 247 | 1.000 | L_{2} | | |
| voloshin-hypergraph_FO1918 | 248 | 1.000 | \chi(\mathcal{H})=\chi | | |
| voloshin-hypergraph_FO1919 | 248 | 1.000 | X=X_{1} \cup X_{2} \cup \ldots \cup X_{\chi} | | |
| voloshin-hypergraph_FO1920 | 248 | 1.000 | L_{i} | | |
| voloshin-hypergraph_FO1921 | 248 | 1.000 | \left|X_{i}\right|-1 | | |
| voloshin-hypergraph_FO1922 | 248 | 1.000 | i=1,2, \ldots, \chi | | |
| voloshin-hypergraph_FO1923 | 248 | 0.562 | |\mathcal{C}|<n-\chi(\mathcal{H}) | | |
| voloshin-hypergraph_FO1924 | 248 | 1.000 | |\mathcal{C}|-n+2 | | |
| voloshin-hypergraph_FO1925 | 248 | 1.000 | T_{i}, i=1,2 | | |
| voloshin-hypergraph_FO1926 | 248 | 0.997 | |\mathcal{D}|=n-1, \quad n-2 \leq|\mathcal{C}| \leq M | | |
| voloshin-hypergraph_FO1927 | 248 | 0.996 | \bar{\chi}(\mathcal{H})=k | | |
| voloshin-hypergraph_FO1928 | 248 | 0.996 | |\mathcal{D}| | | |
| voloshin-hypergraph_FO1929 | 248 | 0.996 | |\mathcal{C}| | | |
| voloshin-hypergraph_FO1930 | 249 | 1.000 | C=\{x, y, z\} | | |
| voloshin-hypergraph_FO1931 | 249 | 1.000 | \{x, y\},\{y, z\} \in \mathcal{D} | | |
| voloshin-hypergraph_FO1932 | 249 | 1.000 | c(x)=c(z) | | |
| voloshin-hypergraph_FO1933 | 249 | 1.000 | |\mathcal{C}(\mathcal{H}-x)|=|\mathcal{C}(\mathcal{H})|-1 | | |
| voloshin-hypergraph_FO1934 | 249 | 1.000 | \left(x_{n}, x_{n-1}, \ldots, x_{1}\right) | | |
| voloshin-hypergraph_FO1935 | 249 | 0.637 | \mathcal{H}=(X, \mathcal{C}, \mathcal{D}), \sigma | | |
| voloshin-hypergraph_FO1936 | 249 | 1.000 | L_{1}, L_{2} | | |
| voloshin-hypergraph_FO1937 | 250 | 1.000 | L_{i}, i=1,2 | | |
| voloshin-hypergraph_FO1938 | 250 | 1.000 | i:=1 | | |
| voloshin-hypergraph_FO1939 | 250 | 0.965 | i:=3-i | | |
| voloshin-hypergraph_FO1940 | 250 | 0.565 | \sigma= | | |
| voloshin-hypergraph_FO1941 | 250 | 0.999 | T_{1}=L_{1} | | |
| voloshin-hypergraph_FO1942 | 250 | 1.000 | \left\{x_{1}, x_{3}, x_{4}\right\},\left\{x_{4}, x_{3}, x_{5}\right\},\left\{x_{2}, x_{3}, x_{5}\right\} | | |
| voloshin-hypergraph_FO1943 | 250 | 1.000 | \left\{x_{2}, x_{5}\right\} | | |
| voloshin-hypergraph_FO1944 | 250 | 1.000 | x_{1}, x_{2}, x_{4}, x_{3} | | |
| voloshin-hypergraph_FO1945 | 251 | 1.000 | R(\mathcal{H})=(0,1,0, \ldots, 0) | | |
| voloshin-hypergraph_FO1946 | 251 | 0.994 | P(\mathcal{H}, \lambda)=\lambda(\lambda-1) | | |
| voloshin-hypergraph_FO1947 | 252 | 0.995 | \mathcal{K}_{n}^{r}, r \geq 3 | | |
| voloshin-hypergraph_FO1948 | 252 | 0.998 | \mathcal{H}=\left(X, \emptyset,\binom{X}{r}\right) | | |
| voloshin-hypergraph_FO1949 | 252 | 0.972 | \mathcal{H}=\left(X, \emptyset,\binom{X}{2}\right) | | |
| voloshin-hypergraph_FO1950 | 252 | 0.986 | \alpha_{c}(\mathcal{H}) | | |
| voloshin-hypergraph_FO1951 | 252 | 0.976 | \bar{\chi}(\mathcal{H})=\alpha_{c}(\mathcal{H}) | | |
| voloshin-hypergraph_FO1952 | 252 | 1.000 | \chi(G) \geq \omega(G) | | |
| voloshin-hypergraph_FO1953 | 253 | 1.000 | \bar{\chi} \geq k+1 | | |
| voloshin-hypergraph_FO1954 | 253 | 1.000 | X=\{1,2, \ldots, 2 k+5\} | | |
| voloshin-hypergraph_FO1955 | 253 | 1.000 | C_{1}=\{1,2,3\}, C_{2}=\{1,4,5\}, \ldots, C_{k+2}=\{1,2 k+4,2 k+5\} | | |
| voloshin-hypergraph_FO1962 | 253 | 0.957 | \mathcal{H}=\left(X,\binom{X}{r}, \mathcal{D}\right), r \geq 2 | | |
| voloshin-hypergraph_FO1963 | 253 | 0.998 | \bar{\chi}\left(\mathcal{H}_{Y}\right)=r-1=\alpha_{c}\left(\mathcal{H}_{Y}\right) | | |
| voloshin-hypergraph_FO1964 | 253 | 0.998 | |Y| \geq r | | |
| voloshin-hypergraph_FO1965 | 253 | 0.998 | \bar{\chi}\left(\mathcal{H}_{Y}\right)=|Y|=\alpha_{c}\left(\mathcal{H}_{Y}\right) | | |
| voloshin-hypergraph_FO1966 | 253 | 0.998 | |Y|<r | | |
| voloshin-hypergraph_FO1967 | 254 | 0.570 | \bar{\chi}(\mathcal{H})=n-1=\alpha_{\mathcal{C}}(\mathcal{H}) | | |
| voloshin-hypergraph_FO1968 | 254 | 0.904 | \bar{\chi}\left(\mathcal{H}_{Y}\right)=|Y|-1=\alpha_{\mathcal{C}}\left(\mathcal{H}_{Y}\right) | | |
| voloshin-hypergraph_FO1969 | 254 | 0.904 | \bar{\chi}\left(\mathcal{H}_{Y}\right)=|Y|=\alpha_{\mathcal{C}}\left(\mathcal{H}_{Y}\right) | | |
| voloshin-hypergraph_FO1970 | 254 | 0.793 | \tau\left(\mathcal{H}_{C}\right) | | |
| voloshin-hypergraph_FO1971 | 254 | 0.998 | \tau_{2}\left(\mathcal{H}_{\mathcal{C}}\right) | | |
| voloshin-hypergraph_FO1972 | 254 | 0.997 | \tau\left(\mathcal{H}_{\mathcal{C}}\right)=1 | | |
| voloshin-hypergraph_FO1973 | 254 | 0.997 | \tau_{2}\left(\mathcal{H}_{\mathcal{C}}\right) \geq 3 | | |
| voloshin-hypergraph_FO1974 | 254 | 0.977 | \tau_{2}\left(\mathcal{H}_{\mathcal{C}}\right)=2 | | |
| voloshin-hypergraph_FO1975 | 254 | 0.982 | \alpha_{c}(\mathcal{H})=|X|-1 | | |
| voloshin-hypergraph_FO1976 | 254 | 1.000 | |X|-2 | | |
| voloshin-hypergraph_FO1977 | 254 | 1.000 | \bar{\chi}(\mathcal{H}) \leq|X|-2 | | |
| voloshin-hypergraph_FO1978 | 254 | 1.000 | \bar{\chi}(\mathcal{H}) \neq | | |
| voloshin-hypergraph_FO1979 | 254 | 0.899 | \boldsymbol{\alpha}_{c}(\mathcal{H}) | | |
| voloshin-hypergraph_FO1980 | 254 | 0.997 | \mathcal{H}=(X, \mathcal{C}),|X|=n \geq 3, r \geq 2 | | |
| voloshin-hypergraph_FO1981 | 254 | 0.844 | C_{n}^{r} | | |
| voloshin-hypergraph_FO1982 | 254 | 0.844 | X=\{0,1, \ldots, n-1\} | | |
| voloshin-hypergraph_FO1983 | 254 | 0.844 | \mathcal{C}=\{\{i, i+1(\bmod n), \ldots, i+r- | | |
| voloshin-hypergraph_FO1984 | 254 | 1.000 | 1(\bmod n)\}: i=0,1, \ldots, n-1\} | | |
| voloshin-hypergraph_FO1985 | 254 | 1.000 | C_{n}=(X, E) | | |
| voloshin-hypergraph_FO1986 | 254 | 1.000 | r-1 | | |
| voloshin-hypergraph_FO1987 | 254 | 1.000 | C_{n}^{2} | | |
| voloshin-hypergraph_FO1988 | 254 | 0.614 | C_{5}^{3} | | |
| voloshin-hypergraph_FO1989 | 254 | 0.614 | \left(X, C_{5}^{3}, \emptyset\right) | | |
| voloshin-hypergraph_FO1990 | 254 | 0.995 | C_{n}^{r}=(X, \mathcal{C}), 3 \leq r \leq n | | |
| voloshin-hypergraph_FO1991 | 254 | 0.995 | 2 r \geq n+2 | | |
| voloshin-hypergraph_FO1992 | 255 | 1.000 | r=n | | |
| voloshin-hypergraph_FO1993 | 255 | 1.000 | r \leq n-1 | | |
| voloshin-hypergraph_FO1994 | 255 | 1.000 | \left|C_{i} \cap C_{j}\right| \geq 2, i, j \in I | | |
| voloshin-hypergraph_FO1995 | 255 | 1.000 | \left\{x_{3}, x_{4}\right\} | | |
| voloshin-hypergraph_FO1996 | 255 | 1.000 | C_{i} \in \mathcal{C} | | |
| voloshin-hypergraph_FO1997 | 255 | 1.000 | \left|C_{i} \cap\left\{x_{1}, x_{2}\right\}\right| \geq 2 | | |
| voloshin-hypergraph_FO1998 | 255 | 1.000 | \left|C_{i} \cap\left\{x_{3}, x_{4}\right\}\right| \geq 2 | | |
| voloshin-hypergraph_FO1999 | 255 | 1.000 | \bar{\chi}\left(C_{n}^{r}\right)<n-1 | | |
| voloshin-hypergraph_FO2000 | 255 | 1.000 | x_{3}, x_{4} | | |
| voloshin-hypergraph_FO2001 | 255 | 1.000 | n-4 | | |
| voloshin-hypergraph_FO2002 | 255 | 1.000 | \bar{\chi}\left(C_{n}^{r}\right)=n-2 | | |
| voloshin-hypergraph_FO2003 | 255 | 1.000 | \tau\left(C_{n}^{r}\right)=2 | | |
| voloshin-hypergraph_FO2004 | 255 | 1.000 | \alpha\left(C_{n}^{r}\right)=n-2=\bar{\chi}\left(C_{n}^{r}\right) | | |
| voloshin-hypergraph_FO2005 | 255 | 1.000 | 2 r=n+1 | | |
| voloshin-hypergraph_FO2006 | 255 | 1.000 | r=3,4 | | |
| voloshin-hypergraph_FO2007 | 255 | 1.000 | r \geq 5 | | |
| voloshin-hypergraph_FO2008 | 255 | 1.000 | \alpha\left(C_{n}^{r}\right)=n-2 | | |
| voloshin-hypergraph_FO2009 | 255 | 1.000 | \bar{\chi}\left(C_{n}^{r}\right)<n-2 | | |
| voloshin-hypergraph_FO2010 | 255 | 0.988 | x_{1}, x_{2} \in X | | |
| voloshin-hypergraph_FO2011 | 255 | 1.000 | n_{i j} | | |
| voloshin-hypergraph_FO2012 | 255 | 1.000 | x_{j}, i, j=1,2,3,4 | | |
| voloshin-hypergraph_FO2013 | 255 | 1.000 | n_{12}=0 | | |
| voloshin-hypergraph_FO2014 | 255 | 1.000 | n_{34}=0 | | |
| voloshin-hypergraph_FO2015 | 255 | 0.942 | \left|C \cap\left\{x_{1}, x_{2}\right\}\right| \leq 1 | | |
| voloshin-hypergraph_FO2016 | 255 | 0.942 | \left|C \cap\left\{x_{3}, x_{4}\right\}\right| \leq 1 | | |
| voloshin-hypergraph_FO2017 | 255 | 1.000 | n_{12}+n_{34} \geq 1 | | |
| voloshin-hypergraph_FO2018 | 255 | 1.000 | n_{12}+n_{23}+n_{34}+n_{41}+4=n=2 r-1 | | |
| voloshin-hypergraph_FO2019 | 255 | 1.000 | 2 r-1+n_{12}+n_{34}<2 r | | |
| voloshin-hypergraph_FO2020 | 255 | 1.000 | r<r | | |
| voloshin-hypergraph_FO2021 | 255 | 1.000 | C_{2 r-1}^{r} | | |
| voloshin-hypergraph_FO2022 | 255 | 1.000 | r \geq 3 | | |
| voloshin-hypergraph_FO2023 | 255 | 1.000 | x_{1}, x_{2}, x_{3} | | |
| voloshin-hypergraph_FO2024 | 255 | 1.000 | x_{j}, i, j=1,2,3 | | |
| voloshin-hypergraph_FO2025 | 255 | 1.000 | n_{12}+n_{23}+n_{31}+3=n=2 r-1 | | |
| voloshin-hypergraph_FO2026 | 256 | 1.000 | r<5 | | |
| voloshin-hypergraph_FO2027 | 256 | 1.000 | 2 r \leq n | | |
| voloshin-hypergraph_FO2028 | 256 | 0.995 | \mathcal{H}^{r}=(X, \mathcal{C}) | | |
| voloshin-hypergraph_FO2029 | 256 | 1.000 | 2 r+2 | | |
| voloshin-hypergraph_FO2030 | 256 | 1.000 | 2 r | | |
| voloshin-hypergraph_FO2031 | 256 | 0.978 | C_{2 r} | | |
| voloshin-hypergraph_FO2032 | 256 | 1.000 | C_{2 r-1} | | |
| voloshin-hypergraph_FO2033 | 256 | 1.000 | C_{2}, C_{3}, \ldots, C_{2 r} | | |
| voloshin-hypergraph_FO2034 | 256 | 1.000 | C_{o} | | |
| voloshin-hypergraph_FO2035 | 256 | 0.950 | C_{e} | | |
| voloshin-hypergraph_FO2036 | 256 | 0.950 | \mathcal{H}^{r} | | |
| voloshin-hypergraph_FO2037 | 256 | 0.950 | r+1 | | |
| voloshin-hypergraph_FO2038 | 256 | 0.997 | r=3 | | |
| voloshin-hypergraph_FO2039 | 256 | 0.997 | C_{2}, \ldots, C_{6} | | |
| voloshin-hypergraph_FO2040 | 256 | 0.997 | 2 r-1 | | |
| voloshin-hypergraph_FO2041 | 257 | 0.901 | \alpha\left(\mathcal{H}_{\mathcal{C}}\right)=n-1 | | |
| voloshin-hypergraph_FO2042 | 257 | 0.901 | \bar{\chi}(\mathcal{H})= | | |
| voloshin-hypergraph_FO2043 | 257 | 0.960 | \alpha_{C}(\mathcal{H}) | | |
| voloshin-hypergraph_FO2044 | 257 | 0.998 | \mathcal{H}_{\mathcal{C}}=(X, \mathcal{C}, \emptyset) | | |
| voloshin-hypergraph_FO2045 | 257 | 1.000 | \mathcal{C}_{1} \subseteq \mathcal{C} | | |
| voloshin-hypergraph_FO2046 | 257 | 1.000 | C \cap C^{\prime} \neq \emptyset | | |
| voloshin-hypergraph_FO2047 | 257 | 1.000 | C, C^{\prime} \in \mathcal{C}_{1} | | |
| voloshin-hypergraph_FO2048 | 257 | 1.000 | \left|\bigcap_{C \in \mathcal{C}_{1}}\right| \geq 2 | | |
| voloshin-hypergraph_FO2049 | 257 | 1.000 | \mathcal{C}_{1} | | |
| voloshin-hypergraph_FO2050 | 257 | 0.989 | \left|C \cap C^{\prime}\right| \geq 2 | | |
| voloshin-hypergraph_FO2051 | 257 | 0.989 | C, C^{\prime} \in C | | |
| voloshin-hypergraph_FO2052 | 257 | 0.815 | L\left(\mathcal{H}_{C}\right)=(\mathcal{C}, \mathcal{E}) | | |
| voloshin-hypergraph_FO2053 | 257 | 0.815 | \left(C, C^{\prime}\right) \in \mathcal{E} \Leftrightarrow C \cap C^{\prime} \neq \emptyset | | |
| voloshin-hypergraph_FO2054 | 257 | 0.718 | K_{1}, K_{2}, \ldots, K_{t} | | |
| voloshin-hypergraph_FO2055 | 257 | 0.930 | \tau\left(\mathcal{H}_{\mathcal{C}}\right)=t | | |
| voloshin-hypergraph_FO2056 | 257 | 0.930 | \alpha_{\mathcal{C}}(\mathcal{H})=|X|-t | | |
| voloshin-hypergraph_FO2057 | 258 | 1.000 | \left\{x_{i}, y_{i}\right\} | | |
| voloshin-hypergraph_FO2058 | 258 | 1.000 | K_{i}, i=1,2, \ldots, t | | |
| voloshin-hypergraph_FO2059 | 258 | 1.000 | \left\{x_{i}, y_{i}\right\} \notin \mathcal{D} | | |
| voloshin-hypergraph_FO2060 | 258 | 1.000 | K_{i} \neq K_{j} | | |
| voloshin-hypergraph_FO2061 | 258 | 1.000 | \left\{x_{i}, y_{i}\right\} \cap\left\{x_{j}, y_{j}\right\}= | | |
| voloshin-hypergraph_FO2062 | 258 | 0.961 | x_{1}, y_{1} | | |
| voloshin-hypergraph_FO2063 | 258 | 0.961 | x_{2}, y_{2} | | |
| voloshin-hypergraph_FO2064 | 258 | 0.961 | \ldots, x_{t}, y_{t} | | |
| voloshin-hypergraph_FO2065 | 258 | 0.536 | t+1, t+2, \ldots,|X|-t | | |
| voloshin-hypergraph_FO2066 | 258 | 0.536 | |X|-t=\alpha_{C}(\mathcal{H}) | | |
| voloshin-hypergraph_FO2067 | 258 | 0.447 | \mathrm{v}\left(\mathcal{H}_{C}\right) | | |
| voloshin-hypergraph_FO2068 | 258 | 0.999 | X=\{1,2,3,4,5\}, C=\left\{C_{1}, C_{2}, C_{3}\right\}, C_{1}=\{1,2,3\}, C_{2}=\{2,3,4,5\}, C_{3}=\{1,4,5\} | | |
| voloshin-hypergraph_FO2069 | 258 | 1.000 | C_{1} \cap C_{3}=\{1\} | | |
| voloshin-hypergraph_FO2070 | 258 | 0.934 | \bar{\chi}(\mathcal{H})=\alpha_{C}(\mathcal{H})=3 | | |
| voloshin-hypergraph_FO2071 | 259 | 1.000 | \tau_{2}\left(\mathcal{H}_{1}\right) | | |
| voloshin-hypergraph_FO2072 | 259 | 1.000 | \tau_{2}\left(\mathcal{H}_{2}\right) | | |
| voloshin-hypergraph_FO2073 | 260 | 1.000 | S(\mathcal{H}) | | |
| voloshin-hypergraph_FO2074 | 260 | 1.000 | r_{k}(\mathcal{H})>0 | | |
| voloshin-hypergraph_FO2075 | 260 | 1.000 | \{a, b\} | | |
| voloshin-hypergraph_FO2076 | 260 | 1.000 | a, a^{\prime} | | |
| voloshin-hypergraph_FO2077 | 260 | 1.000 | b, b^{\prime} | | |
| voloshin-hypergraph_FO2078 | 260 | 0.997 | \left\{a, a^{\prime}, b, b^{\prime}\right\} | | |
| voloshin-hypergraph_FO2079 | 260 | 1.000 | a, a^{\prime}, b, b^{\prime} | | |
| voloshin-hypergraph_FO2080 | 260 | 1.000 | \mathcal{H}=\left(X, K_{4}^{3}, K_{4}^{4}\right) | | |
| voloshin-hypergraph_FO2081 | 260 | 1.000 | X=\left\{a, a^{\prime}, b, b^{\prime}\right\} | | |
| voloshin-hypergraph_FO2082 | 261 | 0.949 | a^{\prime} | | |
| voloshin-hypergraph_FO2083 | 261 | 0.949 | b^{\prime} | | |
| voloshin-hypergraph_FO2084 | 261 | 0.999 | \left\{a, a^{\prime}\right\} | | |
| voloshin-hypergraph_FO2085 | 261 | 0.998 | \left\{b, b^{\prime}\right\},\left\{c, c^{\prime}\right\} | | |
| voloshin-hypergraph_FO2086 | 261 | 0.998 | \left\{d, d^{\prime}\right\} | | |
| voloshin-hypergraph_FO2087 | 261 | 1.000 | \left\{a, a^{\prime}, c\right\} | | |
| voloshin-hypergraph_FO2088 | 261 | 0.982 | r_{2} \geq 2 | | |
| voloshin-hypergraph_FO2089 | 261 | 0.982 | r_{4}=1 | | |
| voloshin-hypergraph_FO2090 | 261 | 0.982 | r_{3}=0 | | |
| voloshin-hypergraph_FO2091 | 262 | 0.991 | \left\{a, c, c^{\prime}\right\},\left\{a, d, d^{\prime}\right\},\left\{b, c, c^{\prime}\right\},\left\{b, d, d^{\prime}\right\} | | |
| voloshin-hypergraph_FO2092 | 262 | 1.000 | \mathcal{H}_{2,4} | | |
| voloshin-hypergraph_FO2093 | 262 | 1.000 | S(\mathcal{H})=\{2,4\} | | |
| voloshin-hypergraph_FO2094 | 262 | 1.000 | s, t | | |
| voloshin-hypergraph_FO2095 | 262 | 1.000 | 2 \leq s \leq t-2 | | |
| voloshin-hypergraph_FO2096 | 262 | 1.000 | \mathcal{H}_{s, t} | | |
| voloshin-hypergraph_FO2097 | 262 | 0.998 | S\left(\mathcal{H}_{s, t}\right)=\{s, t\} | | |
| voloshin-hypergraph_FO2098 | 262 | 0.998 | s | | |
| voloshin-hypergraph_FO2099 | 262 | 1.000 | t-1 | | |
| voloshin-hypergraph_FO2100 | 262 | 1.000 | 2 t-s | | |
| voloshin-hypergraph_FO2101 | 262 | 1.000 | 2 t-2 | | |
| voloshin-hypergraph_FO2102 | 262 | 0.723 | \{2, t\} | | |
| voloshin-hypergraph_FO2103 | 262 | 0.723 | \left(X, \emptyset,\binom{X}{2}\right) | | |
| voloshin-hypergraph_FO2104 | 262 | 0.945 | S\left(K_{n}\right)=\{n\} | | |
| voloshin-hypergraph_FO2105 | 262 | 0.945 | K_{t} | | |
| voloshin-hypergraph_FO2106 | 262 | 0.945 | t- | | |
| voloshin-hypergraph_FO2107 | 263 | 0.924 | t=4 | | |
| voloshin-hypergraph_FO2108 | 263 | 0.999 | [m]=\{1, \ldots, m\} | | |
| voloshin-hypergraph_FO2109 | 263 | 1.000 | \mathcal{H}_{2, t} | | |
| voloshin-hypergraph_FO2110 | 263 | 1.000 | x_{r} a_{i} b_{i} | | |
| voloshin-hypergraph_FO2111 | 263 | 1.000 | r \in\{1,2\} | | |
| voloshin-hypergraph_FO2112 | 263 | 1.000 | i \in[t-2] | | |
| voloshin-hypergraph_FO2113 | 263 | 1.000 | a_{i} b_{i} a_{j} b_{j} | | |
| voloshin-hypergraph_FO2114 | 263 | 1.000 | i, j \in[t-2] | | |
| voloshin-hypergraph_FO2115 | 263 | 1.000 | W | | |
| voloshin-hypergraph_FO2116 | 263 | 1.000 | \left\{a_{i}, b_{i}, a_{j}, b_{j}\right\} | | |
| voloshin-hypergraph_FO2117 | 263 | 1.000 | T \cup W | | |
| voloshin-hypergraph_FO2118 | 263 | 1.000 | T \cup U \cup\left\{x_{1} x_{2}\right\} | | |
| voloshin-hypergraph_FO2119 | 263 | 1.000 | S\left(\mathcal{H}_{2, t}\right)=\{2, t\} | | |
| voloshin-hypergraph_FO2120 | 263 | 1.000 | c\left(a_{i}\right) \neq c\left(b_{i}\right) | | |
| voloshin-hypergraph_FO2121 | 263 | 1.000 | a_{i} | | |
| voloshin-hypergraph_FO2122 | 263 | 1.000 | b_{i} | | |
| voloshin-hypergraph_FO2123 | 263 | 0.987 | c\left(a_{i}\right)=c\left(x_{1}\right)=1 | | |
| voloshin-hypergraph_FO2124 | 263 | 0.987 | c\left(b_{i}\right)=c\left(x_{2}\right)=2 | | |
| voloshin-hypergraph_FO2125 | 263 | 1.000 | c\left(a_{i}\right)=c\left(b_{i}\right) | | |
| voloshin-hypergraph_FO2126 | 263 | 1.000 | \left\{x_{1} x_{2}\right\} | | |
| voloshin-hypergraph_FO2127 | 263 | 1.000 | \left(X_{1}, \mathcal{C}_{1}, \mathcal{D}_{1}\right) | | |
| voloshin-hypergraph_FO2128 | 263 | 0.739 | \left(X_{2}, \mathcal{C}_{2}, \mathcal{D}_{2}\right) | | |
| voloshin-hypergraph_FO2129 | 263 | 0.739 | (X, C, \mathcal{D}) | | |
| voloshin-hypergraph_FO2130 | 263 | 0.998 | X=X_{1} \cup X_{2}, \mathcal{C}=\mathcal{C}_{1} \cup \mathcal{C}_{2} | | |
| voloshin-hypergraph_FO2131 | 263 | 0.998 | \mathcal{D}=\mathcal{D}_{1} \cup \mathcal{D}_{2} \cup R | | |
| voloshin-hypergraph_FO2132 | 263 | 0.991 | \left\{i+j: i \in S\left(\mathcal{H}_{1}\right), j \in S\left(\mathcal{H}_{2}\right)\right\} | | |
| voloshin-hypergraph_FO2133 | 263 | 1.000 | z \notin X | | |
| voloshin-hypergraph_FO2134 | 263 | 1.000 | \left(r_{1}, r_{2}, \ldots, r_{n}\right) | | |
| voloshin-hypergraph_FO2135 | 263 | 1.000 | R\left(\mathcal{H}^{\prime}\right)=\left(0, r_{1}, r_{2}, \ldots, r_{n}\right) | | |
| voloshin-hypergraph_FO2136 | 263 | 1.000 | n \geq | | |
| voloshin-hypergraph_FO2137 | 264 | 1.000 | n<2 t-s | | |
| voloshin-hypergraph_FO2138 | 264 | 0.996 | s+1 | | |
| voloshin-hypergraph_FO2139 | 264 | 0.999 | K_{s+1} | | |
| voloshin-hypergraph_FO2140 | 264 | 1.000 | n \geq 2 t-s | | |
| voloshin-hypergraph_FO2141 | 264 | 1.000 | s=2 | | |
| voloshin-hypergraph_FO2142 | 264 | 1.000 | s>2 | | |
| voloshin-hypergraph_FO2143 | 264 | 0.996 | K_{s-2} | | |
| voloshin-hypergraph_FO2144 | 264 | 0.996 | \mathcal{H}_{2, t-s+2} | | |
| voloshin-hypergraph_FO2145 | 264 | 1.000 | \{s-2\}+\{2, t-s+2\}=\{s, t\} | | |
| voloshin-hypergraph_FO2146 | 264 | 1.000 | s-2+2(t-s+2)-2= | | |
| voloshin-hypergraph_FO2147 | 264 | 1.000 | t-1>s \geq 2 | | |
| voloshin-hypergraph_FO2148 | 264 | 1.000 | s \geq 2 | | |
| voloshin-hypergraph_FO2149 | 264 | 1.000 | t \geq 4 | | |
| voloshin-hypergraph_FO2150 | 264 | 1.000 | t-s \geq 2 | | |
| voloshin-hypergraph_FO2151 | 264 | 1.000 | n \geq t+(t-s) \geq 6 | | |
| voloshin-hypergraph_FO2152 | 264 | 0.999 | 7 \mathcal{C} | | |
| voloshin-hypergraph_FO2153 | 264 | 0.999 | 6 \mathcal{D} | | |
| voloshin-hypergraph_FO2154 | 264 | 0.615 | X=\{1,2,3,4,5,6\}, C=\{\{1,2,3\} | | |
| voloshin-hypergraph_FO2155 | 264 | 0.783 | \{1,4,5\},\{6,2,3\},\{6,4,5\},\{2,3,4\},\{3,4,5\},\{2,4,5\}\}, \mathcal{D}=\{\{1,6\},\{1,2,3\},\{1,4,5\} | | |
| voloshin-hypergraph_FO2156 | 264 | 0.906 | X, \emptyset, \emptyset | | |
| voloshin-hypergraph_FO2157 | 264 | 1.000 | \{1, \ldots, n\} | | |
| voloshin-hypergraph_FO2158 | 265 | 0.990 | X^{\prime}=\bigcup_{v \in X}\left\{v^{-}, v^{+}\right\} | | |
| voloshin-hypergraph_FO2159 | 265 | 0.957 | D^{\prime}=\bigcup_{v \in D}\left\{v^{-}, v^{+}\right\} | | |
| voloshin-hypergraph_FO2160 | 265 | 0.957 | C^{\prime}=\left\{v^{-}: v \in C\right\} | | |
| voloshin-hypergraph_FO2161 | 265 | 0.999 | \left\{v^{-}, v^{+}, u^{-}\right\} | | |
| voloshin-hypergraph_FO2162 | 265 | 0.999 | \left\{v^{-}, v^{+}, u^{+}\right\} | | |
| voloshin-hypergraph_FO2163 | 265 | 1.000 | \chi(\mathcal{H}) \geq 2 | | |
| voloshin-hypergraph_FO2164 | 265 | 1.000 | S \cup\{2\} | | |
| voloshin-hypergraph_FO2165 | 265 | 0.986 | c\left(v^{-}\right) \neq c\left(v^{+}\right) | | |
| voloshin-hypergraph_FO2166 | 265 | 1.000 | v^{-}, v^{+} | | |
| voloshin-hypergraph_FO2167 | 265 | 1.000 | c\left(v^{-}\right) | | |
| voloshin-hypergraph_FO2168 | 265 | 1.000 | c\left(v^{+}\right) | | |
| voloshin-hypergraph_FO2169 | 265 | 1.000 | c\left(u^{-}\right)=c\left(v^{-}\right) | | |
| voloshin-hypergraph_FO2170 | 265 | 1.000 | c\left(u^{+}\right)=c\left(v^{+}\right) | | |
| voloshin-hypergraph_FO2171 | 265 | 1.000 | c\left(v^{-}\right)=c\left(v^{+}\right) | | |
| voloshin-hypergraph_FO2172 | 265 | 1.000 | \tilde{c} | | |
| voloshin-hypergraph_FO2173 | 265 | 1.000 | \tilde{c}(v)=c\left(v^{-}\right) | | |
| voloshin-hypergraph_FO2174 | 266 | 0.813 | R\left(\mathcal{H}^{\prime}\right) | | |
| voloshin-hypergraph_FO2175 | 266 | 1.000 | n\left(\mathcal{H}^{\prime}\right)=2 n(\mathcal{H}) | | |
| voloshin-hypergraph_FO2176 | 266 | 1.000 | \mathcal{H}(T) | | |
| voloshin-hypergraph_FO2177 | 266 | 1.000 | T=\{t\} | | |
| voloshin-hypergraph_FO2178 | 266 | 1.000 | \mathcal{H}(T)=K_{t} | | |
| voloshin-hypergraph_FO2179 | 266 | 1.000 | |T|>1 | | |
| voloshin-hypergraph_FO2180 | 266 | 1.000 | t=2 | | |
| voloshin-hypergraph_FO2181 | 266 | 1.000 | \mathcal{H}(T-\{2\}) | | |
| voloshin-hypergraph_FO2182 | 266 | 1.000 | t>2 | | |
| voloshin-hypergraph_FO2183 | 266 | 1.000 | K_{t-2} | | |
| voloshin-hypergraph_FO2184 | 266 | 0.999 | \mathcal{H}\left(T^{\prime}\right) | | |
| voloshin-hypergraph_FO2185 | 266 | 0.999 | t-2 | | |
| voloshin-hypergraph_FO2186 | 266 | 0.861 | S=\left\{n_{1}, n_{2}, \ldots, n_{p}\right\} | | |
| voloshin-hypergraph_FO2187 | 266 | 0.861 | n_{1} \geq 2 | | |
| voloshin-hypergraph_FO2188 | 266 | 1.000 | i=n_{p}-1 ; \mathcal{H}=K_{3} | | |
| voloshin-hypergraph_FO2189 | 266 | 0.982 | i \neq 1 | | |
| voloshin-hypergraph_FO2190 | 266 | 0.999 | i \in S | | |
| voloshin-hypergraph_FO2191 | 266 | 0.999 | i \notin S | | |
| voloshin-hypergraph_FO2192 | 266 | 1.000 | i=i-1 | | |
| voloshin-hypergraph_FO2193 | 267 | 1.000 | \mathcal{H}=(X, \mathcal{E}) | | |
| voloshin-hypergraph_FO2194 | 267 | 1.000 | X=\{1,2, \ldots, 6\} | | |
| voloshin-hypergraph_FO2195 | 267 | 0.640 | \mathcal{E} | | |
| voloshin-hypergraph_FO2196 | 267 | 0.640 | R(\mathcal{H})=\left(r_{1}, r_{2}, \ldots, r_{6}\right) | | |
| voloshin-hypergraph_FO2197 | 267 | 0.998 | r_{1}=0, r_{6}=0 | | |
| voloshin-hypergraph_FO2198 | 267 | 0.998 | r_{5} \neq 0 | | |
| voloshin-hypergraph_FO2199 | 267 | 1.000 | r_{4} \neq 0, r_{3} \neq 0, r_{2} \neq 0 | | |
| voloshin-hypergraph_FO2200 | 267 | 1.000 | r_{5}=0 | | |
| voloshin-hypergraph_FO2201 | 267 | 1.000 | r_{4} \neq 0 | | |
| voloshin-hypergraph_FO2202 | 267 | 1.000 | r_{3} \neq 0 | | |
| voloshin-hypergraph_FO2210 | 268 | 0.995 | \{A, B\} | | |
| voloshin-hypergraph_FO2211 | 268 | 1.000 | c(1)=c(2)=A | | |
| voloshin-hypergraph_FO2212 | 268 | 1.000 | c(3)=c(4)=B | | |
| voloshin-hypergraph_FO2213 | 268 | 1.000 | c(5), c(6), c(7) \in\{C, D\} | | |
| voloshin-hypergraph_FO2214 | 268 | 0.999 | \left.R(\mathcal{H})=(0,12,0,3,0,0,0), P(\mathcal{H}, \lambda)=3 \lambda(\lambda-1)\left(\lambda^{2}-5 \lambda+10\right)\right) | | |
| voloshin-hypergraph_FO2215 | 268 | 0.999 | X=\{1,2, \ldots, 7\} | | |
| voloshin-hypergraph_FO2216 | 268 | 0.999 | |\mathcal{E}| \leq 8 | | |
| voloshin-hypergraph_FO2217 | 268 | 1.000 | R(\mathcal{H})=\left(r_{1}, r_{2}, \ldots, r_{7}\right) | | |
| voloshin-hypergraph_FO2218 | 268 | 0.995 | r_{1}=r_{7}=0 | | |
| voloshin-hypergraph_FO2219 | 268 | 0.995 | r_{6} \neq 0 | | |
| voloshin-hypergraph_FO2220 | 268 | 0.995 | r_{6}=0, r_{5} \neq 0 | | |
| voloshin-hypergraph_FO2221 | 268 | 0.960 | r_{7}=r_{6}=r_{5}=0, r_{4} \neq 0 | | |
| voloshin-hypergraph_FO2222 | 268 | 0.531 | \{1,2,7\} \notin \mathcal{E} | | |
| voloshin-hypergraph_FO2223 | 268 | 0.531 | \{3,4,7\} \notin \mathcal{E},\{5,6,7\} \notin \mathcal{E} | | |
| voloshin-hypergraph_FO2224 | 268 | 0.998 | (A, A, B, B, C, C, A) | | |
| voloshin-hypergraph_FO2225 | 268 | 0.998 | (A, A, B, B, C, C, B),(A, A, B, B, C, C, C) | | |
| voloshin-hypergraph_FO2226 | 268 | 1.000 | \{1,2,3\} \notin \mathcal{E},\{1,2,4\} \notin \mathcal{E},\{1,2,5\} \notin \mathcal{E} | | |
| voloshin-hypergraph_FO2227 | 268 | 1.000 | \{3,4,1\},\{3,4,2\} \notin \mathcal{E} | | |
| voloshin-hypergraph_FO2228 | 268 | 0.995 | \{3,4,1\} \in \mathcal{E} | | |
| voloshin-hypergraph_FO2229 | 268 | 0.995 | \{3,4,2\} \in \mathcal{E} | | |
| voloshin-hypergraph_FO2230 | 268 | 0.995 | \{3,4,5\},\{3,4,6\} \notin \mathcal{E} | | |
| voloshin-hypergraph_FO2231 | 268 | 0.745 | \{3,4,5\} \in \mathcal{E} | | |
| voloshin-hypergraph_FO2232 | 268 | 0.996 | \{3,4,6\} \in \mathcal{E} | | |
| voloshin-hypergraph_FO2233 | 268 | 0.996 | \{5,6,1\} \notin \mathcal{E} | | |
| voloshin-hypergraph_FO2234 | 268 | 0.996 | \{5,6,2\} \notin \mathcal{E} | | |
| voloshin-hypergraph_FO2235 | 268 | 0.999 | \{5,6,2\} \in \mathcal{E} | | |
| voloshin-hypergraph_FO2236 | 268 | 0.999 | \{1,2,6\} \in \mathcal{D} | | |
| voloshin-hypergraph_FO2237 | 268 | 1.000 | \{1,2,6\} \notin \mathcal{E} | | |
| voloshin-hypergraph_FO2238 | 268 | 1.000 | \{3,4,1\} \notin \mathcal{E} | | |
| voloshin-hypergraph_FO2239 | 268 | 1.000 | \{3,4,2\} \notin \mathcal{E} | | |
| voloshin-hypergraph_FO2240 | 268 | 0.999 | \{3,4,1\},\{3,4,2\} \in \mathcal{E} | | |
| voloshin-hypergraph_FO2241 | 269 | 0.523 | S\left(\mathcal{H}_{\mathcal{C}}\right) | | |
| voloshin-hypergraph_FO2242 | 269 | 0.523 | S\left(\mathcal{H}_{\mathcal{D}}\right) | | |
| voloshin-hypergraph_FO2243 | 269 | 1.000 | S=\{2,3,5\} | | |
| voloshin-hypergraph_FO2244 | 269 | 1.000 | S(\mathcal{H})=S | | |
| voloshin-hypergraph_FO2245 | 270 | 1.000 | B\left(\mathcal{H}^{\prime}\right) | | |
| voloshin-hypergraph_FO2246 | 270 | 0.991 | B, C | | |
| voloshin-hypergraph_FO2247 | 270 | 0.981 | \mathcal{H}=(X, \mathcal{C}, \mathcal{D})=\left(X,\binom{X}{3},\binom{X}{2}\right) | | |
| voloshin-hypergraph_FO2248 | 270 | 1.000 | X=\{1,2,3\}, \mathcal{C}=\{C\}=\{\{1,2,3\}\}, \mathcal{D}=\left\{D_{1}, D_{2}, D_{3}\right\}= | | |
| voloshin-hypergraph_FO2249 | 270 | 0.991 | \{\{1,2\},\{2,3\},\{1,3\}\} | | |
| voloshin-hypergraph_FO2250 | 270 | 0.991 | f_{1}, f_{2}, f_{3}, f_{4} | | |
| voloshin-hypergraph_FO2251 | 270 | 1.000 | G(\mathcal{H}) | | |
| voloshin-hypergraph_FO2252 | 272 | 1.000 | S(n, k) | | |
| voloshin-hypergraph_FO2253 | 272 | 1.000 | f_{k}\left(G^{*}\right) | | |
| voloshin-hypergraph_FO2254 | 272 | 1.000 | f\left(G^{*}\right)=\sum_{i \geq 1} f_{i}\left(G^{*}\right) | | |
| voloshin-hypergraph_FO2255 | 272 | 1.000 | f_{k-1}\left(G^{*}\right) | | |
| voloshin-hypergraph_FO2256 | 273 | 0.995 | f\left(G^{*}\right) | | |
| voloshin-hypergraph_FO2257 | 273 | 1.000 | k=2 | | |
| voloshin-hypergraph_FO2258 | 273 | 1.000 | \lambda=2 | | |
| voloshin-hypergraph_FO2259 | 273 | 0.994 | S(i, k-1) | | |
| voloshin-hypergraph_FO2260 | 273 | 1.000 | r_{k}(T) | | |
| voloshin-hypergraph_FO2261 | 273 | 1.000 | r_{k}(T)=S(e(T), k-1) | | |
| voloshin-hypergraph_FO2262 | 273 | 1.000 | r_{1}\left(K_{1}\right)=1 | | |
| voloshin-hypergraph_FO2263 | 273 | 1.000 | r_{k}\left(K_{1}\right)=0 | | |
| voloshin-hypergraph_FO2264 | 273 | 1.000 | r_{k}(T)=(k-1) r_{k}(T-x)+r_{k-1}(T-x) | | |
| voloshin-hypergraph_FO2265 | 273 | 1.000 | \lambda(\lambda-1)^{i} | | |
| voloshin-hypergraph_FO2266 | 273 | 1.000 | \bar{\chi}(G)=1+\max \left\{k: f_{k}\left(G^{*}\right) \geq 1\right\} | | |
| voloshin-hypergraph_FO2267 | 273 | 1.000 | \bar{\chi}(G) | | |
| voloshin-hypergraph_FO2268 | 273 | 1.000 | k=\bar{\chi}(G) | | |
| voloshin-hypergraph_FO2269 | 273 | 1.000 | f_{k-1}\left(G^{*}\right) \geq 1 | | |
| voloshin-hypergraph_FO2270 | 273 | 1.000 | S(k-1, i-1) \geq 1 | | |
| voloshin-hypergraph_FO2271 | 273 | 1.000 | 2 \leq i \leq k | | |
| voloshin-hypergraph_FO2272 | 273 | 1.000 | r_{i}(G) \geq 1 | | |
| voloshin-hypergraph_FO2273 | 274 | 1.000 | \bar{\chi}(G)=2 | | |
| voloshin-hypergraph_FO2274 | 274 | 1.000 | u v | | |
| voloshin-hypergraph_FO2275 | 274 | 1.000 | a, b, c | | |
| voloshin-hypergraph_FO2282 | 275 | 0.978 | \mathcal{H}_{2,4}^{\prime}=(X, \mathcal{C}, \mathcal{D}) | | |
| voloshin-hypergraph_FO2283 | 275 | 0.991 | X=\{1,2, \ldots, 6\}, \mathcal{C}=\left\{C_{1}, \ldots, C_{4}\right\}=\{\{1,2,3\},\{2,3,4\},\{2,4,5\},\{4,5,6\}\} | | |
| voloshin-hypergraph_FO2284 | 275 | 0.990 | \mathcal{D}=\left\{D_{1}, \ldots, D_{6}\right\}=\{\{1,2\},\{1,5\},\{1,6\},\{2,4\},\{3,6\},\{4,6\}\} | | |
| voloshin-hypergraph_FO2285 | 275 | 0.990 | \mathcal{H}_{2,4}^{\prime} | | |
| voloshin-hypergraph_FO2286 | 276 | 1.000 | S\left(\mathcal{H}_{2,4}^{\prime}\right)=\{2,4\} | | |
| voloshin-hypergraph_FO2287 | 276 | 1.000 | c(2) \neq c(3) | | |
| voloshin-hypergraph_FO2288 | 276 | 1.000 | \{1,3,4\} \cup\{2,5,6\} | | |
| voloshin-hypergraph_FO2289 | 276 | 1.000 | c(2)=c(3) | | |
| voloshin-hypergraph_FO2290 | 276 | 1.000 | c(4)=c(5) | | |
| voloshin-hypergraph_FO2291 | 276 | 1.000 | c(2) \neq c(4) | | |
| voloshin-hypergraph_FO2292 | 276 | 1.000 | \{1\} \cup\{2,3\} \cup\{4,5\} \cup\{6\} | | |
| voloshin-hypergraph_FO2293 | 276 | 1.000 | \{s, s+1, \ldots, t\} | | |
| voloshin-hypergraph_FO2294 | 276 | 0.995 | 1 \leq s \leq 4 | | |
| voloshin-hypergraph_FO2295 | 276 | 0.995 | \{2,4,5, \ldots, t\} | | |
| voloshin-hypergraph_FO2296 | 276 | 0.999 | S(G)=\{\chi(G) | | |
| voloshin-hypergraph_FO2297 | 276 | 1.000 | \chi(G)+1, \ldots, t\} | | |
| voloshin-hypergraph_FO2298 | 277 | 1.000 | \{7, \ldots, t+2\} | | |
| voloshin-hypergraph_FO2299 | 277 | 1.000 | \{\{2,3,7\},\{2,3,8\}, \ldots,\{2,3, t+2\}\} | | |
| voloshin-hypergraph_FO2300 | 277 | 1.000 | S \neq \emptyset | | |
| voloshin-hypergraph_FO2301 | 277 | 1.000 | 1 \in S | | |
| voloshin-hypergraph_FO2302 | 277 | 0.999 | \{4,5, \ldots, t\} \subset S\left(\mathcal{H}^{\prime}\right) \subset S | | |
| voloshin-hypergraph_FO2303 | 277 | 1.000 | u, v | | |
| voloshin-hypergraph_FO2304 | 277 | 1.000 | c(u)=c(v) | | |
| voloshin-hypergraph_FO2305 | 277 | 1.000 | \{u, v\} | | |
| voloshin-hypergraph_FO2306 | 277 | 1.000 | c(u) \neq c(v) | | |
| voloshin-hypergraph_FO2307 | 277 | 1.000 | u, v, w | | |
| voloshin-hypergraph_FO2308 | 277 | 1.000 | c(u)=c(v) \neq c(w) | | |
| voloshin-hypergraph_FO2309 | 277 | 1.000 | \{v, w\} | | |
| voloshin-hypergraph_FO2310 | 277 | 1.000 | S(G)= | | |
| voloshin-hypergraph_FO2311 | 277 | 0.990 | \{\chi(G), \chi(G)+1, \ldots, t\} | | |
| voloshin-hypergraph_FO2312 | 277 | 0.990 | \{4,5, \ldots, t\} \subset S\left(\mathcal{H}^{\prime}\right) | | |
| voloshin-hypergraph_FO2313 | 279 | 1.000 | Z_{1}, Z_{2} | | |
| voloshin-hypergraph_FO2314 | 279 | 1.000 | Z_{3} | | |
| voloshin-hypergraph_FO2315 | 279 | 1.000 | Z_{1} | | |
| voloshin-hypergraph_FO2316 | 279 | 1.000 | Z_{2} | | |
| voloshin-hypergraph_FO2317 | 279 | 0.793 | b, c\} | | |
| voloshin-hypergraph_FO2318 | 279 | 1.000 | \left\{Z_{1}, Z_{2}, Z_{3}, a, b, c\right\} | | |
| voloshin-hypergraph_FO2319 | 279 | 1.000 | \mathcal{C}=\left\{\left\{Z_{1}, a, c\right\},\left\{Z_{2}, a, b\right\},\left\{Z_{3}, b, c\right\}\right\} | | |
| voloshin-hypergraph_FO2320 | 279 | 1.000 | \left\{Z_{1}, a, c\right\} | | |
| voloshin-hypergraph_FO2321 | 279 | 0.998 | \chi(\mathcal{H})=\bar{\chi}(\mathcal{H})= | | |
| voloshin-hypergraph_FO2322 | 280 | 1.000 | R(\mathcal{H})=(0,0,3,0,0,0) | | |
| voloshin-hypergraph_FO2323 | 280 | 1.000 | P(\mathcal{H}, \lambda)=3 \lambda(\lambda- | | |
| voloshin-hypergraph_FO2324 | 280 | 0.780 | 1)(\lambda-2) | | |
| voloshin-hypergraph_FO2325 | 280 | 0.780 | \left(Z_{1}, Z_{2}, Z_{3}\right) | | |
| voloshin-hypergraph_FO2326 | 280 | 1.000 | (a, b, c),(c, b, c),(c, a, c) | | |
| voloshin-hypergraph_FO2327 | 280 | 0.995 | n=4 | | |
| voloshin-hypergraph_FO2328 | 280 | 0.995 | X=\left\{x_{1}, x_{2}, x_{3}\right. | | |
| voloshin-hypergraph_FO2329 | 280 | 0.987 | \left.x_{4}\right\} | | |
| voloshin-hypergraph_FO2330 | 280 | 0.987 | m=5 | | |
| voloshin-hypergraph_FO2331 | 280 | 0.987 | Y=\left\{y_{1}, y_{2}, y_{3}\right. | | |
| voloshin-hypergraph_FO2332 | 280 | 1.000 | \left.y_{4}, y_{5}\right\} | | |
| voloshin-hypergraph_FO2333 | 280 | 1.000 | S\left(x_{i}\right) \subseteq Y | | |
| voloshin-hypergraph_FO2334 | 280 | 1.000 | S_{1}=\left\{y_{1}\right\} | | |
| voloshin-hypergraph_FO2335 | 280 | 1.000 | S_{2}=\left\{y_{1}, y_{2}, y_{3}\right\} | | |
| voloshin-hypergraph_FO2336 | 280 | 1.000 | S_{3}=\left\{y_{3}, y_{4}\right\} | | |
| voloshin-hypergraph_FO2337 | 280 | 1.000 | S_{4}=\left\{y_{2}, y_{4}, y_{5}\right\} | | |
| voloshin-hypergraph_FO2338 | 280 | 1.000 | x_{1}, x_{2}, x_{4} | | |
| voloshin-hypergraph_FO2339 | 281 | 1.000 | S_{1} \cap S_{2} \neq \emptyset | | |
| voloshin-hypergraph_FO2340 | 281 | 1.000 | D_{1}= | | |
| voloshin-hypergraph_FO2341 | 281 | 0.999 | S_{2} \cap S_{3} \neq \emptyset | | |
| voloshin-hypergraph_FO2342 | 281 | 0.999 | D_{2}=\left\{x_{2}, x_{3}\right\} | | |
| voloshin-hypergraph_FO2343 | 281 | 0.999 | S_{2} \cap S_{4} \neq \emptyset | | |
| voloshin-hypergraph_FO2344 | 281 | 1.000 | D_{3}=\left\{x_{2}, x_{4}\right\} | | |
| voloshin-hypergraph_FO2345 | 281 | 1.000 | S_{3} \cap S_{4} \neq \emptyset | | |
| voloshin-hypergraph_FO2346 | 281 | 0.993 | D_{4}=\left\{x_{3}, x_{4}\right\} | | |
| voloshin-hypergraph_FO2347 | 281 | 0.993 | S_{1} \cap S_{3}=\emptyset | | |
| voloshin-hypergraph_FO2348 | 281 | 0.993 | S_{1} \cap S_{4}=\emptyset | | |
| voloshin-hypergraph_FO2349 | 281 | 1.000 | C_{1}=\left\{x_{1}, x_{2}, x_{3}\right\}, C_{2}= | | |
| voloshin-hypergraph_FO2350 | 281 | 1.000 | \left\{x_{1}, x_{2}, x_{4}\right\} | | |
| voloshin-hypergraph_FO2351 | 281 | 1.000 | \mathcal{C}=\left\{C_{1}, C_{2}\right\}, \mathcal{D}=\left\{D_{1}, D_{2}, D_{3}, D_{4}\right\} | | |
| voloshin-hypergraph_FO2352 | 283 | 0.998 | n=1,2,3, \ldots | | |
| voloshin-hypergraph_FO2353 | 283 | 0.998 | P_{1}, P_{2}, \ldots | | |
| voloshin-hypergraph_FO2354 | 283 | 1.000 | P_{1} | | |
| voloshin-hypergraph_FO2355 | 283 | 1.000 | P_{k} | | |
| voloshin-hypergraph_FO2356 | 283 | 1.000 | P_{k+1} | | |
| voloshin-hypergraph_FO2357 | 283 | 1.000 | n=1,2, \ldots | | |
| voloshin-hypergraph_FO2358 | 283 | 1.000 | P_{k} \rightarrow P_{k+1} | | |
| voloshin-hypergraph_FO2359 | 283 | 1.000 | P_{n}, n | | |
| voloshin-hypergraph_FO2360 | 283 | 1.000 | P_{1} \rightarrow P_{2} | | |
| voloshin-hypergraph_FO2361 | 283 | 1.000 | P_{2} \rightarrow P_{3} | | |
| voloshin-hypergraph_FO2362 | 283 | 1.000 | P_{n_{0}} | | |
| voloshin-hypergraph_FO2363 | 283 | 1.000 | n_{0}=3 | | |
| voloshin-hypergraph_FO2364 | 283 | 1.000 | n_{0}=4 | | |
| voloshin-hypergraph_FO2365 | 284 | 1.000 | k+1 | | |
| voloshin-hypergraph_FO2366 | 284 | 1.000 | n \geq n_{0} | | |
| voloshin-hypergraph_FO2367 | 285 | 1.000 | P_{3} | | |
| voloshin-hypergraph_FO2368 | 285 | 1.000 | P_{1}, P_{2}, \ldots, P_{k} \rightarrow P_{k+1} | | |
| voloshin-hypergraph_FO2369 | 285 | 1.000 | P_{2}, P_{3}, \ldots, P_{k-1} | | |
| voloshin-hypergraph_FO2370 | 285 | 1.000 | f(n) | | |
| voloshin-hypergraph_FO2371 | 285 | 1.000 | g(n) | | |
| voloshin-hypergraph_FO2372 | 285 | 1.000 | f(n) \leq g(n) | | |
| voloshin-hypergraph_FO2373 | 285 | 1.000 | n \geq N_{1} | | |
| voloshin-hypergraph_FO2374 | 285 | 1.000 | f(n) / c_{1} \leq g(n) / c_{2} | | |
| voloshin-hypergraph_FO2375 | 285 | 1.000 | n \geq N_{2} | | |
| voloshin-hypergraph_FO2376 | 285 | 1.000 | f(n) \leq C g(n) | | |
| voloshin-hypergraph_FO2377 | 285 | 1.000 | C=c_{1} / c_{2} | | |
| voloshin-hypergraph_FO2378 | 285 | 1.000 | C^{\prime} \geq C | | |
| voloshin-hypergraph_FO2379 | 285 | 1.000 | N \geq N_{2} | | |
| voloshin-hypergraph_FO2380 | 285 | 1.000 | n \geq N | | |
| voloshin-hypergraph_FO2381 | 285 | 1.000 | O(g(n) | | |
| voloshin-hypergraph_FO2382 | 285 | 0.999 | =O(g(n))) | | |
| voloshin-hypergraph_FO2383 | 285 | 1.000 | O(g(n)) | | |
| voloshin-hypergraph_FO2384 | 285 | 1.000 | g(n)=n | | |
| voloshin-hypergraph_FO2385 | 285 | 1.000 | O(n) | | |
| voloshin-hypergraph_FO2386 | 286 | 1.000 | O\left(n^{k}\right) | | |
| voloshin-hypergraph_FO2387 | 286 | 1.000 | O\left(a^{n}\right) | | |
| voloshin-hypergraph_FO2388 | 286 | 1.000 | a>1 | | |
| voloshin-hypergraph_FO2389 | 286 | 1.000 | O(1) | | |
| voloshin-hypergraph_FO2390 | 286 | 1.000 | O(\log n) | | |
| voloshin-hypergraph_FO2391 | 286 | 1.000 | O(n!) | | |
| voloshin-hypergraph_FO2392 | 286 | 0.798 | \left(n^{2}-n\right) / 2 | | |
| voloshin-hypergraph_FO2393 | 286 | 1.000 | O\left(n^{2}\right) | | |
| voloshin-hypergraph_FO2394 | 286 | 1.000 | m n | | |
| voloshin-hypergraph_FO2395 | 286 | 0.974 | O(m n) | | |
| voloshin-hypergraph_FO2396 | 286 | 1.000 | O | | |
| voloshin-hypergraph_FO2397 | 286 | 1.000 | n\left(G_{1}\right)=4, m\left(G_{1}\right)=3, n\left(G_{2}\right)=5, m\left(G_{2}\right)=7, n\left(G_{3}\right)=8, m\left(G_{3}\right)=12 | | |
| voloshin-hypergraph_FO2398 | 286 | 1.000 | G_{1}:(1,1,1,3), G_{2}:(2,2,2,4,4), G_{3}:(2,2,3,3,3,3,4,4) | | |
| voloshin-hypergraph_FO2399 | 286 | 1.000 | L\left(G_{1}\right)=\{\{2\},\{1,3,4\},\{2,4\},\{2,3\}\} | | |
| voloshin-hypergraph_FO2400 | 287 | 0.998 | J\left(G_{1}\right)=\{\{1,2\},\{2,3\},\{3,4\},\{2,4\}\} | | |
| voloshin-hypergraph_FO2401 | 287 | 1.000 | G_{5}, G_{6}, G_{7}, G_{8}, G_{9} | | |
| voloshin-hypergraph_FO2402 | 287 | 0.999 | G_{1} \cong G_{2}, G_{3} \cong G_{4}, G_{7} \cong G_{8} \cong G_{9} | | |
| voloshin-hypergraph_FO2403 | 287 | 1.000 | \eta(T)=2, \eta\left(C_{5}\right)=3, \eta\left(W_{5}\right)=4, \eta\left(K_{2,3}=3\right. | | |
| voloshin-hypergraph_FO2404 | 287 | 1.000 | K_{4,4}: C_{4}, C_{8} | | |
| voloshin-hypergraph_FO2405 | 287 | 1.000 | C_{4}, C_{8} | | |
| voloshin-hypergraph_FO2406 | 287 | 1.000 | C_{5}, C_{9} | | |
| voloshin-hypergraph_FO2407 | 287 | 0.890 | \omega\left(G_{1}\right)=\omega\left(G_{2}\right)=\omega\left(G_{3}\right)=\omega\left(G_{4}\right)=3, \omega\left(G_{5}\right)=\omega\left(G_{6}\right)=\omega\left(G_{7}\right)=\omega\left(G_{8}\right)=\omega\left(G_{9}\right)=2 | | |
| voloshin-hypergraph_FO2408 | 287 | 1.000 | \alpha\left(G_{1}\right)=\alpha\left(G_{2}\right)=\alpha\left(G_{3}\right)=\alpha\left(G_{4}\right)=2, \alpha\left(G_{5}\right)=\alpha\left(G_{6}\right)=4 | | |
| voloshin-hypergraph_FO2409 | 287 | 0.803 | \boldsymbol{\alpha}\left(G_{7}\right)=\boldsymbol{\alpha}\left(G_{8}\right)=\boldsymbol{\alpha}\left(G_{9}\right)=3 | | |
| voloshin-hypergraph_FO2410 | 287 | 0.803 | \boldsymbol{\tau}\left(G_{1}\right)=\boldsymbol{\tau}\left(G_{2}\right)=2, \boldsymbol{\tau}\left(G_{3}\right)= | | |
| voloshin-hypergraph_FO2411 | 287 | 0.997 | \tau\left(G_{4}\right)=3, \tau\left(G_{5}\right)=\tau\left(G_{6}\right)=4, \tau\left(G_{7}\right)=\tau\left(G_{8}\right)=\tau\left(G_{9}\right)=2 | | |
| voloshin-hypergraph_FO2412 | 287 | 0.995 | \nu\left(G_{1}\right)=\nu\left(G_{2}\right)=\nu\left(G_{3}\right)=\nu\left(G_{4}\right)=2, \nu\left(G_{5}\right)=\nu\left(G_{6}\right)=4, \nu\left(G_{7}\right)=\nu\left(G_{8}\right)=\nu\left(G_{9}\right)=2 | | |
| voloshin-hypergraph_FO2413 | 287 | 1.000 | \alpha\left(C_{n}\right)=\tau\left(C_{n}\right)=\nu\left(C_{n}\right)=n / 2 | | |
| voloshin-hypergraph_FO2414 | 287 | 1.000 | \alpha\left(C_{n}\right)=\nu\left(C_{n}\right)=(n-1) / 2 | | |
| voloshin-hypergraph_FO2415 | 287 | 1.000 | \tau\left(C_{n}\right)=(n+1) / 2 | | |
| voloshin-hypergraph_FO2416 | 287 | 1.000 | n: \omega\left(C_{n}\right)=2 | | |
| voloshin-hypergraph_FO2417 | 287 | 0.905 | \Lambda\left(E_{n}\right)=0, \Lambda\left(C_{n}\right)=1, \Lambda\left(K_{n}\right)=(n-1)(n-2) / 2, \Lambda\left(W_{n}\right)=n-1 | | |
| voloshin-hypergraph_FO2418 | 287 | 0.782 | \operatorname{diam}(T)=9 | | |
| voloshin-hypergraph_FO2419 | 287 | 0.782 | =5 | | |
| voloshin-hypergraph_FO2420 | 287 | 0.604 | =28 | | |
| voloshin-hypergraph_FO2421 | 287 | 0.604 | =49 | | |
| voloshin-hypergraph_FO2422 | 287 | 0.745 | m=n | | |
| voloshin-hypergraph_FO2423 | 287 | 0.745 | \tau\left(K_{m, n}\right)=\nu\left(K_{m, n}\right)=\min \{m, n\} | | |
| voloshin-hypergraph_FO2424 | 287 | 0.745 | \tau=\nu=13 | | |
| voloshin-hypergraph_FO2425 | 288 | 0.646 | \Theta\left(G_{1}\right)=\alpha\left(G_{1}\right)=3, \Theta\left(G_{2}\right)= | | |
| voloshin-hypergraph_FO2426 | 288 | 0.544 | \boldsymbol{\alpha}\left(G_{2}\right)=5, \boldsymbol{\theta}\left(G_{3}\right)=\boldsymbol{\alpha}\left(G_{3}\right)=3 | | |
| voloshin-hypergraph_FO2427 | 288 | 0.987 | M\left(G_{1}\right)=3, \omega\left(G_{1}\right)-1=2 ; M\left(G_{2}\right)=4, \omega\left(G_{2}\right)-1=2 ; M\left(G_{3}\right)=2, \omega\left(G_{3}\right)-1=2.2 | | |
| voloshin-hypergraph_FO2428 | 288 | 1.000 | M\left(C_{n}\right)=2, M\left(K_{n}\right)=n-1, M\left(W_{n}\right)=3 | | |
| voloshin-hypergraph_FO2429 | 288 | 1.000 | M(G)=3 | | |
| voloshin-hypergraph_FO2430 | 288 | 1.000 | \leq k-1 | | |
| voloshin-hypergraph_FO2431 | 288 | 0.934 | \operatorname{diam}(G)=6 | | |
| voloshin-hypergraph_FO2432 | 288 | 1.000 | n=3,4, K_{n} | | |
| voloshin-hypergraph_FO2433 | 288 | 1.000 | n \geq 3, W_{n} | | |
| voloshin-hypergraph_FO2434 | 288 | 1.000 | n=4,5 | | |
| voloshin-hypergraph_FO2435 | 288 | 0.999 | G_{1}: 5 ; G_{2}: 7 | | |
| voloshin-hypergraph_FO2436 | 288 | 0.427 | K_{3,3}: 0,1,2,3 | | |
| voloshin-hypergraph_FO2437 | 288 | 0.427 | K_{5}: 0,1,2,3,4 | | |
| voloshin-hypergraph_FO2438 | 288 | 1.000 | K_{n}: n=3,4 ; K_{m, n}: m=1, n \geq 3 | | |
| voloshin-hypergraph_FO2439 | 288 | 1.000 | m=2, n \geq 3 ; W_{n}: n \geq 4 | | |
| voloshin-hypergraph_FO2440 | 288 | 1.000 | \chi\left(E_{n}\right)=1, \chi\left(K_{n}\right)=n, \chi\left(K_{m, n}\right)=2, \chi\left(T_{n}\right)=2, \chi\left(C_{2 n}\right)=2, \chi\left(C_{2 n+1}\right)=3, \chi\left(W_{2 n}\right)=4 | | |
| voloshin-hypergraph_FO2441 | 288 | 0.928 | \chi\left(W_{2 n+1}\right)=3 | | |
| voloshin-hypergraph_FO2442 | 288 | 0.928 | \lambda \geq 136 | | |
| voloshin-hypergraph_FO2443 | 288 | 0.928 | \chi(G)=5 | | |
| voloshin-hypergraph_FO2444 | 288 | 1.000 | P\left(E_{4}, \lambda\right)=\lambda^{4} ; P\left(C_{5}, \lambda\right)=(\lambda-1)^{5}-(\lambda-1) ; P\left(W_{4}, \lambda\right)=\lambda^{(4)} ; P\left(P_{n}, \lambda\right)=\lambda(\lambda-1)^{n-1} | | |
| voloshin-hypergraph_FO2445 | 288 | 1.000 | S(7,1)=1, S(7,2)=63, S(7,3)=301, S(7,4)=350, S(7,5)=140, S(7,6)=21 | | |
| voloshin-hypergraph_FO2446 | 288 | 0.999 | S(7,7)=1 ; s(3,1)=2, s(3,2)=-3, s(3,3)=1 | | |
| voloshin-hypergraph_FO2447 | 288 | 0.999 | P\left(G_{1}, \lambda\right)=\lambda(\lambda-1)^{3}(\lambda-2)^{2}\left(\lambda^{2}-\right. | | |
| voloshin-hypergraph_FO2448 | 288 | 1.000 | 3 \lambda+3)^{2} ; P\left(G_{2}, \lambda\right)=\lambda(\lambda-1)(\lambda-2)^{4} ; P\left(G_{3}, \lambda\right)=\lambda(\lambda-1)(\lambda-2)^{4}\left(\lambda^{2}-3 \lambda+3\right) | | |
| voloshin-hypergraph_FO2449 | 289 | 1.000 | L(G)=\{\{2,4\} | | |
| voloshin-hypergraph_FO2450 | 289 | 0.970 | \{1,3,4,5\},\{2,5\},\{1,2,5\},\{2,3,4\}\} | | |
| voloshin-hypergraph_FO2451 | 289 | 0.970 | 1,2,3,4,5 | | |
| voloshin-hypergraph_FO2452 | 289 | 1.000 | M=3 | | |
| voloshin-hypergraph_FO2453 | 289 | 1.000 | \chi \leq 4 | | |
| voloshin-hypergraph_FO2454 | 289 | 1.000 | W_{2 k-1} | | |
| voloshin-hypergraph_FO2455 | 289 | 1.000 | W_{2 k} | | |
| voloshin-hypergraph_FO2456 | 289 | 1.000 | \chi^{\prime}\left(K_{n}\right)=n | | |
| voloshin-hypergraph_FO2457 | 289 | 1.000 | \chi^{\prime}\left(K_{n}\right)=n-1 | | |
| voloshin-hypergraph_FO2458 | 289 | 1.000 | \chi^{\prime}\left(C_{n}\right)=3 | | |
| voloshin-hypergraph_FO2459 | 289 | 0.997 | \chi^{\prime}\left(C_{n}\right)=2 | | |
| voloshin-hypergraph_FO2460 | 289 | 0.997 | \chi^{\prime}\left(W_{n}\right)=n-1 | | |
| voloshin-hypergraph_FO2461 | 289 | 0.997 | n \geq 4 . \chi^{\prime}\left(K_{m, n}\right)=\max \{m, n\} | | |
| voloshin-hypergraph_FO2462 | 289 | 0.973 | \bar{\chi}^{\prime}(G)=8 | | |
| voloshin-hypergraph_FO2463 | 289 | 0.973 | \bar{\chi}^{\prime}\left(C_{n}\right)=1, \bar{\chi}^{\prime}\left(W_{n}\right)=n-1 | | |
| voloshin-hypergraph_FO2464 | 289 | 0.973 | \bar{\chi}^{\prime}=7 | | |
| voloshin-hypergraph_FO2465 | 289 | 0.973 | \bar{\chi}^{\prime}=6 | | |
| voloshin-hypergraph_FO2466 | 289 | 1.000 | \bar{\chi}^{\prime}=5 | | |
| voloshin-hypergraph_FO2467 | 289 | 1.000 | K_{n}: n \geq 3 ; K_{m, n}: m=n ; W_{n}: n \geq 4 | | |
| voloshin-hypergraph_FO2468 | 289 | 0.998 | n\left(\mathcal{H}_{1}\right)=6, m\left(\mathcal{H}_{1}\right)=5 ; n\left(\mathcal{H}_{2}\right)=6, m\left(\mathcal{H}_{2}\right)=11 | | |
| voloshin-hypergraph_FO2469 | 289 | 1.000 | \Delta\left(\mathcal{H}_{1}\right)=3, \Delta\left(\mathcal{H}_{2}\right)=5 | | |
| voloshin-hypergraph_FO2470 | 289 | 1.000 | r\left(\mathcal{H}_{1}\right)=3 ; r\left(\mathcal{H}_{2}\right)=4 | | |
| voloshin-hypergraph_FO2471 | 289 | 1.000 | \mathcal{H}: N(1)=\{2,4\}, N(2)=\{1,3,4,5\}, N(3)=\{2,4,5\}, N(4)=\{1,2,3,5\} | | |
| voloshin-hypergraph_FO2472 | 289 | 0.773 | N(5)=\{2,3,4\}, N(6)=\emptyset | | |
| voloshin-hypergraph_FO2473 | 289 | 0.773 | \mathcal{H}^{*}: N\left(d_{1}\right)=\left\{d_{2}, d_{3}\right\}, N\left(d_{2}\right)=\left\{d_{1}, d_{3}, d_{4}\right\}, N\left(d_{3}\right)= | | |
| voloshin-hypergraph_FO2474 | 289 | 0.493 | \left\{d_{1}, d_{2}, d_{4}, d_{5}\right\}, N\left(d_{4}\right)=\left\{d_{2}, d_{3}, d_{5}\right\}, N\left(d_{5}\right)=\left\{d_{3}, d_{4}\right\} | | |
| voloshin-hypergraph_FO2475 | 289 | 0.493 | r(\mathcal{H})=r\left(\mathcal{H}^{*}\right)=3.7 . L(G)= | | |
| voloshin-hypergraph_FO2476 | 289 | 0.398 | \{\{1,5\},\{1,2\},\{2,3\},\{2,4\},\{4,5\}\} ; L\left(G^{*}\right)=\{\{a, b\},\{b, c, d\},\{c\},\{d, e\},\{a, e\}\} .9 . E_{n}^{*} | | |
| voloshin-hypergraph_FO2477 | 290 | 1.000 | L\left(K_{4}^{3}\right)=\{\{1,2,3\},\{1,3,4\},\{2,3,4\},\{1,2,4\}\} | | |
| voloshin-hypergraph_FO2478 | 290 | 1.000 | 1 \rightarrow 7 \rightarrow 11 \rightarrow 6 | | |
| voloshin-hypergraph_FO2479 | 290 | 0.990 | S=\{3,4,5,6,7,8,10,11,13,14\} | | |
| voloshin-hypergraph_FO2480 | 290 | 0.990 | \alpha(\mathcal{H})=10 | | |
| voloshin-hypergraph_FO2481 | 290 | 0.927 | T=\{1,2,9,12,15\} | | |
| voloshin-hypergraph_FO2482 | 290 | 0.927 | \tau(\mathcal{H})=5 | | |
| voloshin-hypergraph_FO2483 | 290 | 0.927 | \mathcal{D}^{\prime}=\{\{6,11,15\} | | |
| voloshin-hypergraph_FO2484 | 290 | 0.279 | \{9,13,14\},\{1,3,7\},\{2,8,4\}\} . \mathbf{1 0} . \boldsymbol{v}(\mathcal{H})=4 | | |
| voloshin-hypergraph_FO2485 | 290 | 0.279 | \boldsymbol{\rho}(\mathcal{H})=6 | | |
| voloshin-hypergraph_FO2486 | 290 | 0.971 | \tau\left(\mathcal{H}_{1}\right)=2, \alpha\left(\mathcal{H}_{1}\right)=4, \nu\left(\mathcal{H}_{1}\right)=2 ; \tau\left(\mathcal{H}_{2}\right)=3, \alpha\left(\mathcal{H}_{2}\right)=5, \nu\left(\mathcal{H}_{2}\right)=3 | | |
| voloshin-hypergraph_FO2487 | 290 | 1.000 | \wedge\left(\mathcal{H}_{1}\right)=1, \wedge\left(\mathcal{H}_{2}\right)=0 | | |
| voloshin-hypergraph_FO2488 | 290 | 1.000 | K_{n}: n=1,2 ; K_{m, n}: m, n \geq 1 ; W_{n} | | |
| voloshin-hypergraph_FO2489 | 290 | 0.326 | \mathcal{D}=\{\{1,2,3\},\{1,2,4\},\{2,3,4\}\} | | |
| voloshin-hypergraph_FO2490 | 290 | 0.326 | X=\{1,2,3\} | | |
| voloshin-hypergraph_FO2491 | 290 | 0.326 | \mathcal{D}=\{\{1,2,3\} | | |
| voloshin-hypergraph_FO2492 | 290 | 1.000 | \{1,2\},\{2,3\},\{1,3\}\} | | |
| voloshin-hypergraph_FO2493 | 290 | 1.000 | P_{n}, n \geq 1 | | |
| voloshin-hypergraph_FO2494 | 290 | 1.000 | X=\{1,2,3,4\}, \mathcal{D}= | | |
| voloshin-hypergraph_FO2495 | 290 | 0.513 | \{\{1,4\},\{2,4\},\{3,4\}\} | | |
| voloshin-hypergraph_FO2496 | 290 | 0.513 | X=\{1,2,3,4\}, \mathcal{D}=\{\{1,4\},\{2,4\},\{3,4\}\} | | |
| voloshin-hypergraph_FO2497 | 290 | 0.644 | L\left(\mathcal{H}_{2}\right)=C_{5} | | |
| voloshin-hypergraph_FO2498 | 290 | 1.000 | \chi^{\prime}\left(\mathcal{H}_{1}\right)=3 ; \chi^{\prime}\left(\mathcal{H}_{2}\right)=3 | | |
| voloshin-hypergraph_FO2499 | 291 | 0.259 | \alpha(\mathcal{H})=6 ; \tau(\mathcal{H})=2 | | |
| voloshin-hypergraph_FO2500 | 291 | 0.259 | \gamma(\mathcal{H})=4.5 | | |
| voloshin-hypergraph_FO2501 | 291 | 0.817 | M(\mathcal{H})=2, \chi(\mathcal{H}) \geq 3 | | |
| voloshin-hypergraph_FO2502 | 291 | 0.713 | \chi(\mathcal{H})=2, \bar{\chi}(\mathcal{H})=3 | | |
| voloshin-hypergraph_FO2503 | 291 | 0.713 | \chi\left(\mathcal{H}_{\mathcal{C}}\right)=1, \bar{\chi}\left(\mathcal{H}_{\mathcal{C}}\right)=3 ; \chi\left(\mathcal{H}_{\mathcal{D}}\right)=2, \bar{\chi}\left(\mathcal{H}_{\mathcal{D}}\right)=5 | | |
| voloshin-hypergraph_FO2504 | 291 | 0.693 | \bar{\chi}(\mathcal{H}) \geq 3 | | |
| voloshin-hypergraph_FO2505 | 291 | 1.000 | P\left(\mathcal{H}_{1}, \lambda\right)=3 \lambda^{(3)}+6 \lambda^{(2)}, R\left(\mathcal{H}_{1}\right)=(0,6,3,0) ; P\left(\mathcal{H}_{2}, \lambda\right)=\lambda^{(2)}, R\left(\mathcal{H}_{2}\right)=(0,1,0,0) | | |
| voloshin-hypergraph_FO2506 | 291 | 0.577 | \chi\left(\mathcal{H}_{\mathcal{D}}\right)=3, \bar{\chi}\left(\mathcal{H}_{C}\right)=3 | | |
| voloshin-hypergraph_FO2507 | 291 | 0.278 | \alpha_{\mathcal{C}}\left(\mathcal{H}_{1}\right)=3, \bar{\chi}\left(\mathcal{H}_{1}\right)=3 ; \alpha_{\mathcal{C}}\left(\mathcal{H}_{2}\right)=3, \bar{\chi}\left(\mathcal{H}_{2}\right)=3 | | |
| voloshin-hypergraph_FO2508 | 291 | 1.000 | \tau_{2}\left(\mathcal{H}_{1}\right)=2, \tau_{2}\left(\mathcal{H}_{2}\right)=3 | | |
| voloshin-hypergraph_FO2509 | 291 | 0.962 | S\left(\mathcal{H}_{\mathcal{C}}\right)=\{1,2,3,4,5,6\}, S\left(\mathcal{H}_{\mathcal{D}}\right)=\{2,3,4,5,6,7,8\} | | |
| voloshin-hypergraph_FO2510 | 291 | 0.962 | S(\mathcal{H})=\{2,3,4,5\} | | |
| voloshin-hypergraph_FO2511 | 291 | 1.000 | n \rightarrow \infty | | |
| voloshin-hypergraph_FO2512 | 292 | 1.000 | \overline{C_{k}} | | |
| voloshin-hypergraph_FO2513 | 292 | 0.966 | (n, k, \lambda) | | |
| voloshin-hypergraph_FO2514 | 292 | 1.000 | m(G) / n(G) | | |
| voloshin-hypergraph_FO2515 | 292 | 1.000 | |X|=|\mathcal{D}|=r^{2}-r+ | | |
| voloshin-hypergraph_FO2516 | 293 | 1.000 | f: V\left(G_{1}\right) \rightarrow V\left(G_{2}\right) | | |
| voloshin-hypergraph_FO2517 | 293 | 1.000 | n>m | | |
| voloshin-hypergraph_FO2518 | 293 | 1.000 | R(p, q) | | |
| voloshin-hypergraph_FO2519 | 293 | 1.000 | K_{p} | | |
| voloshin-hypergraph_FO2520 | 293 | 1.000 | K_{q} | | |
| voloshin-hypergraph_FO2521 | 293 | 1.000 | R(3,3)=6 | | |
| voloshin-hypergraph_FO2522 | 294 | 0.996 | S Q S(v) | | |
| voloshin-hypergraph_FO2523 | 294 | 0.996 | S(3,4, v) | | |
| voloshin-hypergraph_FO2524 | 294 | 1.000 | S(t, k, v) | | |
| voloshin-hypergraph_FO2525 | 294 | 1.000 | \mathcal{H}=(X, \mathcal{B}) | | |
| voloshin-hypergraph_FO2526 | 294 | 1.000 | |X|=v | | |
| voloshin-hypergraph_FO2527 | 294 | 0.959 | \operatorname{Tr} \mathcal{H} | | |
| voloshin-hypergraph_FO2528 | 294 | 0.959 | \mathcal{H}=(X, \mathcal{E}), \operatorname{Tr} \mathcal{H}=(X, \mathcal{D}) | | |
| voloshin-hypergraph_FO2529 | 294 | 1.000 | T(n, p, r) | | |
| voloshin-hypergraph_FO2530 | 297 | 0.998 | x, 7 | | |
| voloshin-hypergraph_FO2531 | 297 | 0.998 | \Lambda(G) | | |
| voloshin-hypergraph_FO2532 | 297 | 0.333 | \boldsymbol{\alpha}_{c}(\mathcal{H}), \mathcal{C} | | |
| voloshin-hypergraph_FO2533 | 297 | 0.986 | \kappa(G) | | |
| voloshin-hypergraph_FO2534 | 297 | 0.933 | \tau_{2}\left(\mathcal{H}_{C}\right) | | |
| voloshin-hypergraph_FO2535 | 297 | 0.831 | T, 174 | | |
| voloshin-hypergraph_FO2536 | 297 | 1.000 | m=m(\mathcal{H}) | | |
| voloshin-hypergraph_FO2537 | 297 | 1.000 | r_{i}(\mathcal{H}) | | |
| voloshin-hypergraph_FO2538 | 297 | 0.587 | \alpha_{c}(\mathcal{H}), 236 | | |
| voloshin-hypergraph_FO2539 | 298 | 0.994 | (\mathcal{H})_{2}, 154 | | |
| voloshin-hypergraph_FO2540 | 298 | 0.388 | \mathbf{\tau}_{2}\left(\mathcal{H}_{C}\right), 238 | | |
| voloshin-hypergraph_FO2541 | 298 | 0.793 | \chi^{\prime}(\mathcal{H}), 185 | | |
| voloshin-hypergraph_FO2542 | 298 | 0.813 | \chi(G), 80 | | |
| voloshin-hypergraph_FO2543 | 298 | 0.896 | \chi(\mathcal{H}), 193 | | |
| voloshin-hypergraph_FO2544 | 298 | 0.999 | P(\mathcal{H}, \lambda), 204 | | |
| voloshin-hypergraph_FO2545 | 298 | 0.658 | P(G, \lambda), 80 | | |
| voloshin-hypergraph_FO2546 | 299 | 0.803 | \mathrm{K}(G) | | |
| voloshin-hypergraph_FO2547 | 299 | 0.923 | \Lambda(\mathcal{H}), 179 | | |
| voloshin-hypergraph_FO2548 | 300 | 0.848 | [\mathcal{H}]_{2}, 174 | | |
| voloshin-hypergraph_FO2549 | 300 | 0.772 | \Lambda(\mathcal{H}, T), 174 | | |
| voloshin-hypergraph_FO2550 | 301 | 0.973 | \Delta, 6 | | |
| voloshin-hypergraph_FO2551 | 302 | 0.715 | r(\mathcal{H}) | | |
| voloshin-hypergraph_FO2552 | 303 | 0.516 | \tau(G), 31 | | |
| voloshin-hypergraph_FO2553 | 303 | 0.798 | \bar{\chi}^{\prime}(G), 116 | | |
| voloshin-hypergraph_FO2554 | 303 | 0.988 | w(T), 43 | |