无爪图中子图的度和与Hamilton连通性

The Hamilton-Connectivity with the Sum Degree of Subgraph in Claw-Free Graphs

本文定义了子图的度的概念,并利用子图的度给出如下结果:设G是n阶2-连通无爪图,δ(G) ≥ 3,如果G中任意两个分别同构于P3和K2的不相邻子图H1,H2的度和,对于任意的u,v ÎG,若{u,v}不构成割集,那么u,v间存在Hamilton路。

In this paper, we defined the degree of subgraph, and got the following result on the basis of the degree of subgraph: Let G be a 2-connected claw-free graph of order n, . If H1 and H2, any two non-adjacent subgraphs, are isomorphic to P3 and K2, respectively, and d(H1) + d(H2) ≥ n, for each pair of u,v ÎG, when {u,v} isn’t a cut set, there exists a Hamilton-path in u,v.