On b-coloring of the Kneser graphs

A b-coloring of a graph G by k colors is a proper k-coloring 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 of a graph G, denoted by φ(G), is the maximum k for which G has a b-coloring by k colors. It is obvious that χ(G) ≤ φ(G). A graph G is b-continuous if for every k between χ(G) and φ(G) there is a b-coloring of G by k colors. In this paper, we study the b-coloring of Kneser graphs K(n, k) and determine φ(K(n, k)) for some values of n and k. Moreover, we prove that K(n, 2) is b-continuous for n ≥ 17. © 2009 Elsevier B.V. All rights reserved.