On lower bounds for the b-chromatic number of connected bipartite graphs Mekkia Kouider 2 Laboratoire de Recherche en Informatique (LRI) Universit´ e Paris-Sud Bˆ at. 490, 91405 Orsay, France Mario Valencia-Pabon 3,1 Laboratoire d’Informatique de l’Universit´ e Paris-Nord (LIPN) 99 Av. J.-B. Cl´ ement, 93430 Villetaneuse, France Abstract A b-coloring of a graph G by k colors is a proper k-coloring of the vertices of G such that in each color class there exists a vertex having neighbors in all the other k - 1 color classes. The b-chromatic number χ b (G) of a graph G is the largest integer k such that G admits a b-coloring by k colors. We present some lower bounds for the b-chromatic number of connected bipartite graphs. We also discuss some algorithmic consequences of such lower bounds on some subfamilies of connected bipartite graphs. Keywords: b-chromatic number, lower bounds, bipartite graphs. 1 Supported by Math-AmSud project 10MATH-04 (France-Argentina-Brazil). 2 km@lri.fr 3 valencia@lipn.univ-paris13.fr Electronic Notes in Discrete Mathematics 37 (2011) 399–404 1571-0653/$ – see front matter © 2011 Elsevier B.V. All rights reserved. www.elsevier.com/locate/endm doi:10.1016/j.endm.2011.05.068