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Pré-Publication, Document De Travail Année : 2012

Locally identifying coloring in bounded expansion classes of graphs

Résumé

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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Dates et versions

hal-00768472 , version 1 (21-12-2012)
hal-00768472 , version 2 (10-07-2013)

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Daniel Gonçalves, Aline Parreau, Alexandre Pinlou. Locally identifying coloring in bounded expansion classes of graphs. 2012. ⟨hal-00768472v1⟩
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