不含三角形的IC-可平面图的邻点可区别边染色  

Adjacent Vertex Distinguishing Edge Colorings of Triangle Free IC-planar Graphs

作　　者：宋超 徐常青[1] SONG Chao;XU Changqing(School of Science,Hebei University of Technology,Tianjin,300401,P.R.China)

机构地区：[1]河北工业大学理学院,天津300401

出　　处：《数学进展》2022年第5期817-822,共6页Advances in Mathematics（China）

基　　金：Supported by NSFC(Nos.12071260,12001154)。

摘　　要：图G的k-邻点可区别边染色(简称k-avd染色)是图G的至多使用k个颜色的正常边染色,使得对G中任意相邻的顶点u,v,与u关联的边所染的颜色构成的集合不同于与v关联的边所染的颜色构成的集合.图G的邻点可区别边色数χ'_(a)(G)是G有k-avd染色的最小的整数k.张忠辅等人在[Appl.Math.Lett.,2002,15(5):623-626]中猜想对于任何阶至少为6的连通图G,都有χ'_(a)(G)≤Δ(G)+2.通过权转移方法,本文证明了对于任何Δ(G)≥10的不含三角形的连通IC-可平面图G,都有χ'_(a)(G)≤Δ(G)+2.An adjacent vertex distinguishing k-edge coloring,or k-avd-coloring for short,of a graph G is a proper edge coloring of G using at most k colors such that for every pair of adjacent vertices u,v,the set of colors of the edges incident with u differs from the set of colors of edges incident with v.We denote byχ’_(a)(G)the avd-chromatic number of G which is the smallest integer k such that G can be k-avd-colored.Zhang et al.in[Appl.Math.Lett.,2002,15(5):623-626]conjectured thatχ’_(a)(G)≤Δ(G)+2 for any connected graph G with order at least 6.In this paper,by using the discharging method,we show thatχ’_(a)(G)≤Δ(G)+2 for any triangle free connected IC-planar graph G withΔ(G)>10.

关 键 词：邻点可区别边染色 权转移 IC-可平面图 

分 类 号：O157.5[理学—数学]