On the b-dominating coloring of graphs

The b-chromatic number (G) of a graphG is defined as the largest number k for which the vertices of G can be colored with k colors satisfying the following property: for each i, 1 i k, there exists a vertex xi of color i such that for all j = i, 1 j k there exists a vertex yj of color j adjacent to xi . A graph G is b-perfect if each induced subgraph H of G has (H) = (H), where (H) is the chromatic number of H. We characterize all b-perfect bipartite graphs and all b-perfect P4-sparse graphs byminimal forbidden induced subgraphs.We also prove that every 2K2-free andP5-free graph is b-perfect. © 2005 Published by Elsevier B.V.