线图平方的弱退化  

Weak Degeneracy of the Square of Line Graphs

作　　者：韩铭[1] 何景翔 朱绪鼎 HAN Ming;HE Jingxiang;ZHU Xuding(School of Mathematical Sciences,Zhejiang Normal University,Jinhua,Zhejiang,321004,P.R.Cnina)

机构地区：[1]浙江师范大学数学科学学院,浙江金华321004

出　　处：《数学进展》2024年第4期720-730,共11页Advances in Mathematics（China）

基　　金：Supported by NSFC (Nos.11971438,U20A2068);ZJNSF (Nos.LD19A010001,LY22A010016)。

摘　　要：作为退化的变形,弱退化与退化有很多漂亮的性质.特别地,如果图G是d-弱退化的,那么G是DP-(d+1)-可画的.本文证明了对于任意的图G,如果Δ(G)≤4,则(L(G))^(2)是22-弱退化的,其中(L(G))^(2)为G的线图的平方.由此可知,对于任何Δ(G)≤4的图G,G是强边DP-23-可画的.Weak degeneracy is a variation of degeneracy which shares many nice properties of degeneracy.In particular,if a graph G is weakly d-degenerate,then G is DP-(d+1)-paintable.This paper proves that(L(G))^(2) is weakly 22-degenerate for any graph G withΔ(G)≤4,where(L(G))^(2) is the square of the line graph of G.Consequently,for any graph G withΔ(G)≤4,G is strong edge DP-23-paintable.

关 键 词：弱退化 强边色数 DP-染色 

分 类 号：O157.5[理学—数学]