论文标题
关于常规图的补充的集团行为和螺旋
On the clique behavior and Hellyness of the complements of regular graphs
论文作者
论文摘要
如果集合中的任何一对套件都具有非空交集，则集合的集合正在相交。如果任何相交子集合具有非空交点，则集合\（\ Mathcal {C} \）具有HELLY属性。图是 / helly /如果\（g \）的最大完整子图的集合具有Helly属性。我们证明，如果\（g \）为a \（k \） - 带有\（n \）顶点的常规图，以便\（n> 3K+\ sqrt {2k^{2} {2} -k} \），那么creptiment \（\ bar {g} \）是helly的。我们还考虑了集团图操作员下的螺旋和收敛性的特性是否等于\（k \） - 常规图，对于\（k \）的小值。
A collection of sets is intersecting, if any pair of sets in the collection has nonempty intersection. A collection of sets \(\mathcal{C}\) has the Helly property if any intersecting subcollection has nonempty intersection. A graph is /Helly/ if the collection of maximal complete subgraphs of \(G\) has the Helly property. We prove that if \(G\) is a \(k\)-regular graph with \(n\) vertices such that \(n>3k+\sqrt{2k^{2}-k}\), then the complement \(\bar{G}\) is not Helly. We also consider the problem of whether the properties of Hellyness and convergence under the clique graph operator are equivalent for the complement of \(k\)-regular graphs, for small values of \(k\).
