摘要
令k和n为正整数,G是阶为n的图,并且W⊆ V(G).本文证明了如下结论:对于|W|的任意划分,即|W|=n1+…+nk,其中n1,...,nk为任意的大于等于3的整数,如果W中每个点在G中的最小度至少为2n/3,则G包含k个点不交的圈并且每个圈交W中点的个数分别为n1,…,nk.该结果解决了Wang(2015)提出的猜想,同时推广了Aigner-Brandt定理.
Abstract
Let k and n be positive integers and let G be a graph of order n.Suppose that W is a subset of V(G)with|W|=n1+…+nk such that ni≥3 is any integer for all i.We prove that if the degree of each vertex in W is at least 2n/3,then G contains k vertex disjoint cycles such that each of them intersects W exactly ni vertices for all i.We confirm a conjecture by Wang(2015)and also generalize the Aigner-Brandt theorem.
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