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

作者: 米 晶 , 王江鲁 :山东师范大学数学科学学院,济南;

关键词: 无爪图不相邻子图子图的度Hamilton路Claw-Free Graph Non-Adjacent Subgraph Degree of Subgraph Hamilton-Path

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Gn2-连通无爪图,δ(G) 3,如果G中任意两个分别同构于P3K2的不相邻子图H1H2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} isnt a cut set, there exists a Hamilton-path in u,v.

文章引用: 米 晶 , 王江鲁 (2014) 无爪图中子图的度和与Hamilton连通性。 应用数学进展, 3, 8-16. doi: 10.12677/AAM.2014.31002

参考文献

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[5] Flandrin, E., Fournier, I. and Germa, A. (1988) Circumference and Hamiltonism in K1,3-free graphs. Annals of Discrete Mathematics, 41, 131-140.

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