一类含有两个分支2-因子的无爪图

A Class of Claw-free Graphs Have 2-factor with Two Components

文章主要证明了若图G是阶为n,n>9的连通无爪图,G中至少存在一个非局部连通点或一个单纯点,M(G)={x|x∈V(G),x局部连通}是G的一个连通控制集,则G含有两个分支的2-因子。

Let G be a claw-free graph, IGI〉9, M（G） the set of all vertices of G that have a connected neighborhood,and （M （G）） the induced subgraph of Gon M （G）,we prove that if G has at least a nonconnected neighborhood vertice or a simple vertice, M（G） dominates G and （M（G）） is connected,then Ghave 2-factor with two components.