Graphs with maximum degree Δ≥17 and maximum average degree less than 3 are list 2-distance (Δ+2)-colorable

Marthe Bonamy 1 Benjamin Lévêque 1 Alexandre Pinlou 1
1 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : For graphs of bounded maximum average degree, we consider the problem of 2-distance coloring. This is the problem of coloring the vertices while ensuring that two vertices that are adjacent or have a common neighbor receive different colors. It is already known that planar graphs of girth at least 6 and of maximum degree Δ are list 2-distance (Δ+2)-colorable when Δ≥24 (Borodin and Ivanova (2009)) and 2-distance (Δ+2)-colorable when Δ≥18 (Borodin and Ivanova (2009)). We prove here that Δ≥17 suffices in both cases. More generally, we show that graphs with maximum average degree less than 3 and Δ≥17 are list 2-distance (Δ+2)-colorable. The proof can be transposed to list injective (Δ+1)-coloring.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-01233453
Contributor : Alexandre Pinlou <>
Submitted on : Wednesday, November 25, 2015 - 11:16:51 AM
Last modification on : Friday, February 22, 2019 - 3:45:23 PM

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Marthe Bonamy, Benjamin Lévêque, Alexandre Pinlou. Graphs with maximum degree Δ≥17 and maximum average degree less than 3 are list 2-distance (Δ+2)-colorable. Discrete Mathematics, Elsevier, 2014, 317, pp.19-32. ⟨10.1016/j.disc.2013.10.022⟩. ⟨lirmm-01233453⟩

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