Heavy Cycles in 2-connected Triangle-free Weighted Graphs

作     者：Xue Zheng LV Pei WANG 

作者机构：Department of Mathematics Renmin University of China Department of Mathematics and Physics China University of Petroleum 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2015年第31卷第10期

页      面：1555-1562页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by National Natural Science Foundation of China(Grant No.11001269) 

主　　题：Heavy cycles triangle-free graphs weighted graphs 

摘      要：A weighted graph is one in which every edge e is assigned a nonnegative number, called the weight of e. The sum of the weights of the edges incident with a vertex v is called the weighted degree of v, denoted by dw（v）. The weight of a cycle is defined as the sum of the weights of its edges. Fujisawa proved that if G is a 2-connected triangle-free weighted graph such that the minimum weighted degree of G is at least d, then G contains a cycle of weight at least 2d. In this paper, we proved that if G is a 2-connected triangle-free weighted graph of even size such that dw（u） ＋ dw（v） ≥ 2d holds for any pair of nonadjacent vertices u, v ∈ V（G）, then G contains a cycle of weight at least 2d.