若G是简单图

v(G)是偶数

χ'(G)=?(G)+1

则存在点v∈V(G)

使χ'(G-v)=χ'(G)=?(G)+1.本文对此进行了研究

当图G满足以下条件之一时:(1)设G是含有割边的连通图

χ'(G)=?(G)+1;(2)设G是连通图

κ'(G)=2

G中最多除两个2度顶点外

其它顶点的度数均为k(k>2)

v(G)=2n+2

χ'(G)=?(G)+1;(3)设图G是k正则图

v(G)=2n+2

χ'(G)=?(G)+1;(4)设图G是有2n+2个顶点的连通图

且除点v的度小于k外

其它顶点的度都等于k

χ'(G)=?(G)+1;(5)设图G是有2n+2个顶点的连通图

且除点u

v

d(v) 关键词： 边色数; 正常的k边着色; 正则图; Abstract： If G is a simple graph

and V(G)=2n

then there is a vertex v of G that makes χ'(G-v)=χ'(G)=?(G)+1. So far this conjecture has not been solved. In this paper

we have studied this and proved this conjecture is true when a graph satisfies one of the following conditions:(1) if G is a connected graph with cut edge;(2)if G is a connected graph

κ'(G)=2

except for two 2-degree vertices at most

the degrees of other vertices are k(k>2)

and V(G)=2n+2;(3) if G is a K-regular graph

and V(G)=2n+2;(4) if G is a connected graph with V(G)=2n+2

and the degrees of other vertices are equal to k except a vertex v satisfies d(v) KeyWords： edge chromatic number; normal k-edge coloring; regular graph;