Locally identifying coloring in bounded expansion classes of graphs

Daniel Gonçalves 1 Aline Parreau 2 Alexandre Pinlou 3
1 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
2 DOLPHIN - Parallel Cooperative Multi-criteria Optimization
LIFL - Laboratoire d'Informatique Fondamentale de Lille, Inria Lille - Nord Europe
Abstract : A proper vertex coloring of a graph is said to be locally identifying if the sets of colors in the closed neighborhood of any two adjacent non-twin vertices are distinct. The lid-chromatic number of a graph is the minimum number of colors used by a locally identifying vertex-coloring. In this paper, we prove that for any graph class of bounded expansion, the lid-chromatic number is bounded. Classes of bounded expansion include minor closed classes of graphs. For these latter classes, we give an alternative proof to show that the lid-chromatic number is bounded. This leads to an explicit upper bound for the lid-chromatic number of planar graphs. This answers in a positive way a question of Esperet et al [L. Esperet, S. Gravier, M. Montassier, P. Ochem and A. Parreau. Locally identifying coloring of graphs. Electronic Journal of Combinatorics, 19(2), 2012.].
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Discrete Applied Mathematics, Elsevier, 2013, 161 (18), pp.2946-2951. 〈10.1016/j.dam.2013.07.003〉
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Dernière modification le : jeudi 21 février 2019 - 10:52:49
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Daniel Gonçalves, Aline Parreau, Alexandre Pinlou. Locally identifying coloring in bounded expansion classes of graphs. Discrete Applied Mathematics, Elsevier, 2013, 161 (18), pp.2946-2951. 〈10.1016/j.dam.2013.07.003〉. 〈hal-00768472v2〉

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