The list r-hued coloring of Halin graph

IF 1 3区 数学 Q3 MATHEMATICS, APPLIED
Shudan Lu , Fengxia Liu , Hong-Jian Lai
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引用次数: 0

Abstract

Let L be a list assignment of colors available for vertices of a graph G. An (L,r)-coloring of a graph G is a proper coloring c such that every vertex vV(G) receives at least min{dG(v),r} colors in its neighbors and c(v)L(v). The list r-hued chromatic number χL,r(G) of a graph G, is the smallest k such that for each list assignment L satisfying |L(v)|=k, for any vV(G), G has an (L,r)-coloring. An (L,r)-coloring is called an r-hued k-coloring if L(v)={1,2,,k} for all vV(G). Let G be a Halin graph. We determine the upper bounds of the list r-hued chromatic number of Halin graphs when r=2 and r=Δ. This improves former results on 2-hued coloring of Halin graphs.
哈林图的列表r色着色
设L是图G顶点可用颜色的列表赋值。图G的(L,r)着色是一个适当的着色c,使得每个顶点v∈v (G)在其相邻顶点c(v)∈L(v)中至少得到min{dG(v),r}种颜色。图G的列表色数χL,r(G)是最小的k,使得对于满足|L(v)|=k的每个列表赋值L,对于任意v∈v (G), G具有(L,r)着色。对于所有v∈v (G),如果L(v)={1,2,…,k},则(L,r)着色称为r色k着色。设G是哈林图。我们确定了当r=2和r=Δ时Halin图的列表r色数的上界。这改进了先前关于Halin图的双色着色的结果。
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来源期刊
Discrete Applied Mathematics
Discrete Applied Mathematics 数学-应用数学
CiteScore
2.30
自引率
9.10%
发文量
422
审稿时长
4.5 months
期刊介绍: The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.
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