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On S-packing colourings of distance graphs D(1,t) and D(1,2,t)

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  • Holub, Přemysl
  • Hofman, Jakub

Abstract

For a non-decreasing sequence of positive integers S=(s1,s2,…), the S-packing chromatic numberχS(G) of a graph G is the smallest integer k such that the vertex set of G can be partitioned into subsets Xi, i∈{1,2,…,k}, where vertices in Xi are pairwise at distance greater than Si. By an infinite distance graph with distance set D we mean a graph with vertex set Z in which two vertices i,j are adjacent whenever |i−j|∈D. In this paper we investigate the S-packing chromatic number of infinite distance graphs with distance set D={1,t}, t≥2, and D={1,2,t}, t≥3, for sequences S having all elements from {1,2}.

Suggested Citation

  • Holub, Přemysl & Hofman, Jakub, 2023. "On S-packing colourings of distance graphs D(1,t) and D(1,2,t)," Applied Mathematics and Computation, Elsevier, vol. 447(C).
    • Handle: RePEc:eee:apmaco:v:447:y:2023:i:c:s0096300323000243
    DOI: 10.1016/j.amc.2023.127855
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    References listed on IDEAS

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    1. Daphne Der-Fen Liu & Aileen Sutedja, 2013. "Chromatic number of distance graphs generated by the sets {2,3,x,y}," Journal of Combinatorial Optimization, Springer, vol. 25(4), pages 680-693, May.
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