Packing chromatic number of cubic graphs

József Balogh, Alexandr Kostochka, Xujun Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)

Abstract

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

Original languageEnglish
Pages (from-to)474-483
Number of pages10
JournalDiscrete Mathematics
Volume341
Issue number2
DOIs
Publication statusPublished - Feb 2018
Externally publishedYes

Keywords

  • Cubic graphs
  • Independent sets
  • Packing coloring

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