# Locally identifying coloring of graphs

1 G-SCOP_OC - OC
G-SCOP - Laboratoire des sciences pour la conception, l'optimisation et la production
Abstract : We introduce the notion of locally identifying coloring of a graph. A proper vertex-coloring c of a graph G is said to be locally identifying, if for any adjacent vertices u and v with distinct closed neighborhood, the sets of colors that appear in the closed neighborhood of u and v are distinct. Let $\chi_{lid}(G)$ be the minimum number of colors used in a locally identifying vertex-coloring of G. In this paper, we give several bounds on $\chi_{lid}$ for different families of graphs (planar graphs, some subclasses of perfect graphs, graphs with bounded maximum degree) and prove that deciding whether $\chi_{lid}(G)=3$ for a subcubic bipartite graph $G$ with large girth is an NP-complete problem.
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Cited literature [21 references]

https://hal.archives-ouvertes.fr/hal-00529640
Contributor : Aline Parreau <>
Submitted on : Thursday, May 3, 2012 - 6:21:00 PM
Last modification on : Monday, August 5, 2019 - 3:26:03 PM
Long-term archiving on : Saturday, August 4, 2012 - 2:45:49 AM

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### Identifiers

• HAL Id : hal-00529640, version 2
• ARXIV : 1010.5624

### Citation

Louis Esperet, Sylvain Gravier, Mickael Montassier, Pascal Ochem, Aline Parreau. Locally identifying coloring of graphs. The Electronic Journal of Combinatorics, Open Journal Systems, 2012, 19 (2), pp.40. ⟨hal-00529640v2⟩

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