Dynamic coloring of graphs having no K5 minor

被引：8

作者：

Kim, Younjin ^{[1
]}

Lee, Sang June ^{[2
]}

Oum, Sang-il ^{[3
,4
]}

机构：

[1] Ewha Womans Univ, Dept Math, Seoul, South Korea

[2] Duksung Womens Univ, Dept Math, Seoul, South Korea

[3] Korea Adv Inst Sci & Technol, Dept Math Sci, Daejeon, South Korea

[4] KIAS, Sch Math, Seoul, South Korea

来源：

DISCRETE APPLIED MATHEMATICS | 2016年 / 206卷

基金：

新加坡国家研究基金会;

关键词：

Dynamic coloring; Minor-free graph; Four color theorem; Hadwiger's conjecture; LOCAL CHROMATIC NUMBER; CONJECTURE;

D O I：

10.1016/j.dam.2016.01.022

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that every simple connected graph with no K5 minor admits a proper 4-coloring such that the neighborhood of each vertex v having more than one neighbor is not monochromatic, unless the graph is isomorphic to the cycle of length 5. This generalizes the result on planar graphs by 5.-J. Kim, W.J. Park and the second author [Discrete Appl. Math. 161 (2013) 2207-22121. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：81 / 89

页数：9

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