Some bounds for the b-chromatic number of a graph

Authors:
Mekkia Kouider;Maryvonne Mahéo
Affiliations:
U.M.R. 86-23, Centre d'Orsay, LRI, Bat. 490, Université Paris-Sud XI, 91405 Orsay, Cedex, France;U.M.R. 86-23, Centre d'Orsay, LRI, Bat. 490, Université Paris-Sud XI, 91405 Orsay, Cedex, France
Venue:
Discrete Mathematics
Year:
2002

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Abstract

In this paper we study the b-chromatic number of a graph G. This number is defined as the maximum number k of colors that can be used to color the vertices of G, such that we obtain a proper coloring and each color i has at least one representant xi adjacent to a vertex of every color j, 1 ≤ j ≠ i ≤ k. The main result is the determination of two lower bounds for the b-chromatic number of the cartesian product of two graphs.