【摘要】 设 G是一个图 ,其边集是 E( G) ,E( G)的一个子集 S称为 G的一个边覆盖 ,若 G的每一点都是 S中一条边的端点 .G的一个 (正常 )边覆盖染色是对 G的边进行染色 ,使得每一色组都是 G的一个边覆盖 ,使 G有 (正常 )边覆盖染色所需最多颜色数 ,称为 G的边覆盖色数 ,用χ′c( G)表示 .已知的结果是对于任意简单图 G,都有 δ- 1≤ χ′c( G)≤ δ,δ是 G的最小度 .若 χ′c( G) =δ,则称 G是 CI类的 ;否则称为 CII类的 .本文主要研究了平面图及平衡的完全 r分图的分类问题更多还原

【Abstract】 Let G be a graph with edge set E(G),SE(G) is called a edge cover of G if every vertex of G is an end vertex of an edge in S. The edge covering chromatic number of a graph G, denoted by χ ′ c(G), is the maximum size of a partition of E(G) into edge covers of G. It is known that for any graph G with minimum degree δ,δ-1≤χ ′ c(G)≤δ. We say that G is of CI if χ ′ c(G)=δ, and that G is of CII if χ ′ c(G)=δ-1 for any graph G . Thus we can classify graphs into two types depending on the value of their edge covering chromatic numbers. In this paper, we consider the classification of planar graphs and balanced complete r partite graphs.更多还原