Implicit degree condition for hamiltonicity of 2-heavy graphs

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• 作者：Xing Huang ^{bitmathhuangxing@163.com}
• 关键词：Implicit degree ; Hamilton cycle ; f-implicit-heavy ; 2-heavy
• 刊名：Discrete Applied Mathematics
• 出版年：2017
• 出版时间：11 March 2017
• 年：2017
• 卷：219
• 期：Complete
• 页码：126-131
• 全文大小：403 K
• 卷排序：219

文摘

Let id(v)id(v) denote the implicit degree of a vertex vv in a graph GG. An induced subgraph SS of GG is called f-implicit-heavy if max{id(x),id(y)}≥|V(G)|/2max{id(x),id(y)}≥|V(G)|/2 for every pair of vertices x,y∈V(S)x,y∈V(S) at distance 2 in SS. For a given graph RR, GG is called RR-f-implicit-heavy if every induced subgraph of GG isomorphic to RR is f-implicit-heavy. For a family RR of graphs, GG is called RR-f-implicit-heavy if GG is RR-f-implicit-heavy for every R∈RR∈R. GG is called 2-heavy if there are at least two end-vertices of every induced claw (K1,3K1,3) in GG have degree at least |V(G)|/2|V(G)|/2. In this paper, we prove that: Let GG be a 2-connected 2-heavy graph. If GG is {P7,D}{P7,D}-f-implicit-heavy or {P7,H}{P7,H}-f-implicit-heavy, then GG is hamiltonian.