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 @f(G), is the maximum k for which G has a b-coloring by k colors. It is obvious that @g(G)@?@f(G). A graph G is b-continuous if for every k between @g(G) and @f(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 @f(K(n,k)) for some values of n and k. Moreover, we prove that K(n,2) is b-continuous for n>=17.

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