△(G)=4的Halin-图的邻强边染色

摘要

图G(V,E)的一正常k-边染色f称为G(V,E)的一k-邻强边染色(简称k-ASEC)当且仅当任意uv∈E(G)满足f[u]≠f[v],其中f[u]={f(uw)|uw∈E(G)},并称Xas(G)=min{k|存在G的一k-ASEC}为G的邻强边色数.本文研究了△(G)=4的Halin-图的邻强边染色,得到了如下结果:对△(G)=4的Halin-图有△(G)=4≤Xas(G)≤△(G)+1=5.%A proper k-edge coloring f of graph G(V,E) is said to be a k-adjacent strong edge coloring of graph G(V,E) iff every uv∈ E(G) satisfy f[u]≠f[v], where f[u]= {f (uw) |uw∈ E(G) } ; and xas(G)=min| {f(e) |e∈E} | is called the adjacent strong edge chromatic mumber. In this paper, we study the xas(G)of Halin praphs with △(G)=4.