On b-colorings in regular graphs

Authors:
Mostafa Blidia;Frédéric Maffray;Zoham Zemir
Affiliations:
Département de Mathématiques, Université de Blida, B.P. 270, Blida, Algeria;C.N.R.S, Laboratoire G-SCOP, 46 Avenue Félix Viallet, 38031 Grenoble Cedex, France;Département de Mathématiques, Université de Blida, B.P. 270, Blida, Algeria
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

A b-coloring is a coloring of the vertices of a graph such that each color class contains a vertex that has a neighbor in all other color classes. El-Sahili and Kouider have conjectured that every d-regular graph with girth at least 5 has a b-coloring with d+1 colors. We show that the Petersen graph infirms this conjecture, and we propose a new formulation of this question and give a positive answer for small degree.