Geodesic
Locally identifying coloring of graphs
Louis Esperet1 ; Sylvain Gravier2 ; Mickaël Montassier3 ; Pascal Ochem4 ; Aline Parreau5
1G-SCOP, Grenoble INP, France
2CNRS-Joseph Fourier University, France
3LaBRI, University of Bordeaux, France
4LIRRM-CNRS, University of Montpellier, France
5Institut Fourier, Grenoble University, France
The electronic journal of combinatorics, Tome 19 (2012) no. 2
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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 neighborhoods, the sets of colors that appear in the closed neighborhood of $u$ and $v$, respectively, are distinct. Let $\chi_{\rm{lid}}(G)$ be the minimum number of colors used in a locally identifying vertex-coloring of $G$. In this paper, we give several bounds on $\chi_{\rm{lid}}$ for different families of graphs (planar graphs, some subclasses of perfect graphs, graphs with bounded maximum degree) and prove that deciding whether $\chi_{\rm{lid}}(G)=3$ for a subcubic bipartite graph $G$ with large girth is an NP-complete problem.
DOI : 10.37236/2417
Classification : 05C15, 05C69
Mots-clés : subcubic bipartite graph, identifying code

Louis Esperet  1   ; Sylvain Gravier  2   ; Mickaël Montassier  3   ; Pascal Ochem  4   ; Aline Parreau  5

1 G-SCOP, Grenoble INP, France
2 CNRS-Joseph Fourier University, France
3 LaBRI, University of Bordeaux, France
4 LIRRM-CNRS, University of Montpellier, France
5 Institut Fourier, Grenoble University, France 
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     author = {Louis Esperet and Sylvain Gravier and Micka\"el Montassier and Pascal Ochem and Aline Parreau},
     title = {Locally identifying coloring of graphs},
     journal = {The electronic journal of combinatorics},
     year = {2012},
     volume = {19},
     number = {2},
     doi = {10.37236/2417},
     zbl = {1252.05061},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2417/}
}
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Louis Esperet; Sylvain Gravier; Mickaël Montassier; Pascal Ochem; Aline Parreau. Locally identifying coloring of graphs. The electronic journal of combinatorics, Tome 19 (2012) no. 2. doi: 10.37236/2417

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