摘要
设G是一个简单图,e∈E(G),定义e=uv在G中的度d(e)=d(u)+d(v),其中d(u)和d(v)分别为u和v的度数。若连通图G的每个桥都有一个端点度数为1,则称G是几乎无桥的图。本文的主要结果是:设G是p≥2阶几乎无桥的简单连通图,且GK_(1,p-1)若对任何无公共顶点的两边e_0及e_1,d(e_0)+d(e_1)≥p+4,则G有一个D-闭迹,从而G的线图L(G)是哈密顿的。
Let G be a simple graph, for each edge e=uv of graph G, let d(e)=e(u)+d(u),where d(u) and (v)are degree of the vertices u and v respectively. The main result is asfollows:Let G be a simple connected, almost brideless graph of order p >g,GK_(1,p-1),if d(e_0)+d(e_1)>p+4 for each pair of edges e_0 and e_1 such that v(e_0)∩v(e_1)= , then theline graph L(G) of G has Hamiltonian cycles.
关键词
哈密顿线图
几乎无桥
连通图
简单图
Hamiltonian line graph,D-Circuits, amost bridgeless graph.