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arXiv · 1010.5624

Locally identifying coloring of graphs

Louis Esperet·Sylvain Gravier·Mickael Montassier·Pascal Ochem·Aline Parreau
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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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Louis Esperet, Sylvain Gravier, Mickael Montassier, Pascal Ochem, Aline Parreau. 2010-10-27. Locally identifying coloring of graphs. https://arxiv.org/abs/1010.5624

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