a b s t r a c tA b-coloring of a graph is a coloring such that every color class admits a vertex adjacent to at least one vertex receiving each of the colors not assigned to it. The b-chromaticsubgraph H 1 of G, and every induced subgraph H 2 of H 1 . In this work, we prove that P 4 -tidy graphs (a generalization of many classes of graphs with few induced P 4 s) are b-continuous and b-monotonic. Furthermore, we describe a polynomial time algorithm to compute the b-chromatic number for this class of graphs.