Elsevier

Discrete Mathematics

Volume 341, Issue 2, February 2018, Pages 474-483
Discrete Mathematics

Packing chromatic number of cubic graphs

https://doi.org/10.1016/j.disc.2017.09.014Get rights and content
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Abstract

A packing k-coloring of a graph G is a partition of V(G) into sets V1,,Vk such that for each 1ik the distance between any two distinct x,yVi is at least i+1. The packing chromatic number, χp(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 g2k+2, almost every n-vertex cubic graph of girth at least g has the packing chromatic number greater than k.

Keywords

Packing coloring
Cubic graphs
Independent sets

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