对于部分点度条件下图中点不交的圈猜想的解答  

A solution to the conjecture of vertex disjoint cycles in graphs with partial degree

作　　者：祁玉珍 颜谨[1] Yuzhen Qi;Jin Yan

机构地区：[1]山东大学数学学院,济南250100

出　　处：《中国科学：数学》2024年第11期1829-1850,共22页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:12071260)资助项目。

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.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 jWj=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.

关 键 词：点不交的圈 部分点度 2-因子 划分 

分 类 号：O157.5[理学—数学]