An Implicit Degree Condition for Relative Length of Long Paths and Cycles in Graphs

作     者：Jun-qing CAI Hao LI 

作者机构：School of Management Qufu Normal University L.R.I UMR 8623 CNRS and Universit'e Paris-Sud 11 Institute for Interdisciplinary Research Jianghan University 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2016年第32卷第2期

页      面：365-372页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China(Grant No.11501322) the Postdoctoral Science Foundation of China(Grant No.2015M571999) the Natural Science Foundation of Shandong Province(Grant No.ZR2014AP002) 

主　　题：Hamiltonian path dominating cycles implicit degree longest paths longest cycles 

摘      要：For a graph G, we denote by p（G） and c（G） the number of vertices of a longest path and a longest cycle in G, respectively. For a vertex v in G, id（v） denotes the implicit degree of v. In this paper, we obtain that if G is a 2-connected graph on n vertices such that the implicit degree sum of any three independent vertices is at least n ＋ 1, then either G contains a hamiltonian path, or c（G） 〉 p（G） - 1.