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: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.
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
[1] Bondy, J.A. and Murty, U.S.R. (1976) Graph theory with applications. Macmillan London and Elsevier, New York.
[2] Dirac, G.A. (1952) Some theorems on abstract graphs. Proceedings of the London Mathematical Society, 3, 269-281.
[3] Ore, O. (1960) Note on Hamilton circuits. American Mathematical Monthly, 67, 55.
[4] Matthews, M.M. and Summer, D.P. (1985) Longest paths and cycles in K1,3-free graphs. Graph Theory, 9, 269-277.
[5] Flandrin, E., Fournier, I. and Germa, A. (1988) Circumference and Hamiltonism in K1,3-free graphs. Annals of Discrete Mathematics, 41, 131-140.