Locally identifying coloring of graphs

Louis Esperet (1) , Sylvain Gravier (2) , Mickael Montassier (3) , Pascal Ochem (4) , Aline Parreau (2)

1 G-SCOP - Laboratoire des sciences pour la conception, l'optimisation et la production
2 IF - Institut Fourier
3 LaBRI - Laboratoire Bordelais de Recherche en Informatique
4 LRI - Laboratoire de Recherche en Informatique

A vertex-coloring of a graph G is said to be locally identifying if for any pair (u,v) of adjacent vertices of G, with distinct closed neighborhood, the set of colors that appears in the closed neighborhoods of u and v are distinct. In this paper, we give several bounds on the minimum number of colors needed in such a coloring for different families of graphs (planar graphs, some subclasses of perfect graphs, graphs with bounded maximum degree) and prove that deciding whether a subcubic bipartite graph with large girth has a locally identifying coloring with 3 colors is an NP-complete problem.

Mots clés: distinguishing coloring; identifying code

Domaines: Mathématique discrète [cs.DM]; Combinatoire [math.CO]

Louis Esperet, Sylvain Gravier, Mickael Montassier, Pascal Ochem, Aline Parreau. Locally identifying coloring of graphs. 2010. ⟨hal-00529640v1⟩