On the b-dominating coloring of graphs Original Research Article

The b-chromatic number image of a graph G 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 image, there exists a vertex image of color i such that for all image there exists a vertex image of color j adjacent to image. A graph G is b-perfect if each induced subgraph H of G has image, where image is the chromatic number of H. We characterize all b-perfect bipartite graphs and all b-perfect image-sparse graphs by minimal forbidden induced subgraphs. We also prove that every image-free and image-free graph is b-perfect.