A note on list-coloring powers of graphs

被引：4
|
作者：
Kosar, Nicholas [1 ]
Petrickova, Sarka [1 ]
Reiniger, Benjamin [1 ]
Yeager, Elyse [1 ]
机构：
[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA
来源：
DISCRETE MATHEMATICS | 2014年 / 332卷
基金：
美国国家科学基金会;
关键词：
Choosability; List coloring; Chromatic-choosable; Graph powers;
D O I：
10.1016/j.disc.2014.05.008
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Recently, Kim and Park have found an infinite family of graphs whose squares are not chromatic-choosable. Xuding Zhu asked whether there is some k such that all kth power graphs are chromatic-choosable. We answer this question in the negative: we show that there is a positive constant c such that for any k there is a family of graphs G with chi(G(k)) unbounded and chi(l)(G(k)) >= c chi(G(k)) log chi (G(k)). We also provide an upper bound, chi(l)(G(k)) < chi (G(k))(3) for k > 1. (C) 2014 Elsevier B.V. All rights reserved.
引用
收藏
页码：10 / 14
页数：5
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