【摘要】 给出了如下定理的一个新的简短的证明:若G是一个满足k≥2的k连通赋权图,则G或者包含一个权至少为2m/(k+1)的圈,或者包含一个Hamilton圈,如果以下条件成立:(1)任意k+1个相互独立的顶点的赋权度和至少为m;(2)在G的每个导出爪,导出修正爪和导出P4中,所有边的权都相等.更多还原

【Abstract】 A weighted graph is one in which every edge e is assigned a nonnegative number w（e）,called the weight of e.The weight of a cycle is defined as the sum of the weights of its edges.The weighted degree of a vertex is the sum of the weights of the edges incident with it.This paper gives a short proof of the following theorem:Let G be a k-connected weighted graph where k≥2.Then G contains either a Hamilton cycle or a cycle of weight at least 2m/（k+1）,if G satisfies the following conditions:（1）the weighted degree sum of any k+1 pairwise nonadjacent vertices is at least m;（2）in each induced claw,each induced modified claw and each induced P₄ of G and all edges have the same weight.更多还原