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

摘要: 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 Î G，若{u,v}不构成割集，那么u,v间存在Hamilton路。

Abstract: 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 Î G, when {u,v} isn’t a cut set, there exists a Hamilton-path in u,v.