On -coloring of the Kneser graphs

Abstract: A -coloring of a graph by colors is a proper -coloring of such that in each color class there exists a vertex having neighbors in all the other color classes. The -chromatic number of a graph , denoted by , is the maximum for which has a -coloring by colors. It is obvious that . A graph is -continuous if for every between and there is a -coloring of by colors. In this paper, we study the -coloring of Kneser graphs and determine for some values of and . Moreover, we prove that is -continuous for . [Copyright &y& Elsevier]