摘要
本文证明了设Ｇ为２－连通简单权图．若对任一ｕｖ∈Ｅ（Ｇ），ｗ（ｕ）＋ｗ（ｖ）＞ｋ；且满足下列 条件之一：（ｉ）Ｇ为二部图，且任一ｅ∈Ｅ（Ｇ），ｗ（ｅ）＞０；（ｉｉ）Ｇ的连通度为２；（ｉｉｉ）Ｇ为阶数不小 于６的３正则图；（ｉｖ）Ｇ为阶数不小于６的轮形图，则Ｇ含圈Ｃ使ｗ（ｃ）＞ｋ．另外，本文还找到 了一些２－连通权图Ｇ．对任一ｕｖ∈Ｅ（Ｇ）．ｗ（ｕ）＋ｗ（ｖ）＞ｋ，但Ｇ不含权至少为ｋ的圈，且其最优 圈不都是Ｈａｍｉｌｔｏｎ圈．
Let G be a 2-connected graph with ω(u)+ω(v)>k for every pair of nonadjacent vertices u and v. If G satisfies one of the following conditions: (i) G is a bipartite graph; and for every e∈E(G), w(e)>0; (ii) the connectivity of G is two; (iii) G is a 3-regular graph with |V(G)|>6; (iv) G is a wheel graph with |V(G)|>6 then G contains a cycle of weight at least k. In addition, 2-connected weighted graphs G with ω(u)+ω(v)>k for ev- ery pair of nonadjacent, vertices u and v had been found. But G neither contains a cycle of weight at least k, nor every optinal cycle is a Hamilton cycle.
出处
《福州大学学报（自然科学版）》
CAS
CSCD
1992年第1期16-20,共5页
Journal of Fuzhou University(Natural Science Edition)
