长圈的邻域交条件的推广

A Generalization of a Neighborhood Intersection Condition for Long Cycles

证明了若G为一个k(k≥2)连通简单图,独立数为α,V(G)=n≥3,X1,X2,…,Xk是顶点集合V的子集,X=X1∪X2∪…∪Xk,且对于Xi(i=1,2,…,k)中任意两个不相邻点u,v,|N(u)∩N(v)|≥α,则X在G中可圈,并给出几个相关推论.

This paper has proved that if a simple graph G of order n（≥3） is k-connected （（k≥2） and such that for each i,i=1,2,… ,k, and for each pair of nonadjacent vertices u,v∈Xi, where X1 ,X2 ,… ,Xk are subsets of the vertex set V and X=X1∪X2∪…∪Xk , we have N（u）∩N（v）｜≥α, where a is independent number of G, then G is X-cyclable. Moreover, it gives some propositions.