k-对等图的邻集和最小度

Neighborhood Unions and Minimum Degree for k-Uniform Graphs

证明了如下结论 :设G是阶数为n的二边连通的简单图 ,k≥ 2 ,k·n是偶数 ,并且n>4k + 1- 4 k .假设对V(G)的所有非空独立子集X都有 ｜N(X) ｜≥(k- 1)n+｜X｜+ 12k - 1并且δ(G) >(k- 1) (n+ 2 ) + 12k - 1,则G是k 对等图 .

The following result is proved. Let G be a 2 edge connected simple graph of order n, k·n(k≥2) even number and n>4k+1-4k,and assume |N(X)|≥(k-1)n+|X|+12k-1 for each nonempty independent subset X in V(G) and δ(G)>(k-1)(n+2)+12k-1, then G is k uniform.