长圈的邻域并条件的推广

A Generalization of a Neighboring Union(intersection) Condition for Long Cycles

本文证明了若G为一个k(k≥2)连通简单图,最小度为,δV(G)=n≥3,X 1,X 2,……,X k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,都有N(u)∪N(v)≥n-δ,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 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）｜≥n-δ , where δ is minimum degree of G , then G is X-cyclable .Moreover, we give some propositions.