2017/03/29 by József Balogh, Balogh, József, Alexandr Kostochka +3 · 1 citation
Computer Science · Mathematics · #05C15 #05C35 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #math.CO #msc:05C15 #msc:05C35
paper · pdf · doi:10.48550/arxiv.1703.09873
16 pages, 2 figures
openalex publication_date 2017/03/29 · arxiv created 2017/03/30 · arxiv updated 2017/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A packing k-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.