Packing chromatic number of cubic graphs

被引：34

作者：

Balogh, Jozsef ^{[1
]}

Kostochka, Alexandr ^{[1
,2
]}

Liu, Xujun ^{[1
]}

机构：

[1] Univ Illinois, Dept Math, Champaign, IL 61820 USA

[2] Sobolev Inst Math, Novosibirsk 630090, Russia

来源：

DISCRETE MATHEMATICS | 2018年 / 341卷 / 02期

基金：

美国国家科学基金会; 俄罗斯基础研究基金会;

关键词：

Packing coloring; Cubic graphs; Independent sets; REGULAR GRAPHS;

D O I：

10.1016/j.disc.2017.09.014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A packing k-coloring of a graph G is a partition of V(G) into sets V-1,...,V-k such that for each 1 <= i <= k the distance between any two distinct x, y is an element of V-i is at least i + 1. The packing chromatic number, chi(p)(G), of a graph G is the minimum k such that G has a packing k-coloring. Sloper showed that there are 4-regular graphs with arbitrarily large packing chromatic number. The question whether the packing chromatic number of subcubic graphs is bounded appears in several papers. We answer this question in the negative. Moreover, we show that for every fixed k and g >= 2k + 2, almost every n-vertex cubic graph of girth at least g has the packing chromatic number greater than k. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：474 / 483

页数：10

共 22 条

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[Anonymous], THESIS

[2] The packing coloring problem for lobsters and partner limited graphs [J].