一类图中D-闭迹存在的充分条件

A Sufficient Condition for the Existence of Dominating Circuits in Some Graph

设G是一个简单图,(?)e∈E(G),定义e=uv的度d(e)=d(u)+d(v),其中d(u)和d(v)分别为u和v的度。本文的主要结果是:设G是n≥3阶几乎无桥的简单连通图,且G≠K_(1(?)n-1),G不含C_3和C_4,若对任何三个相互点不交的边e_0,e_1和e_2,d(e_0)+d(e_1)+d(e_2)≥n+7,则G有一个D-闭迹,从而G的线图L(G)是哈密顿图。

For every edge e=uv of a graph G, Let d(e)=d(u)+e(v), where d(u) and d(v) are degrees of the vertices u and v respectively. Our main result is as follows: Let G be a simple connected almost bridgless graph of order n≥3, G(?)K_(1,n-1), and suppose that there are no C_3 and C_4 3n G. If the degree-sum of any three mutually nonadjacent edges of G is at least n+7, then G has a D-Circuit.