The achromatic number of Kneser graphs

Abstract The achromatic number α of a graph is the largest number of colors that can be assigned to its vertices such that adjacent vertices have different color and every pair of different colors appears on the end vertices of some edge. We estimate the achromatic number of Kneser graphs K ( n , k ) and determine α ( K ( n , k ) ) for some values of n and k. Furthermore, we study the achromatic number of some geometric type Kneser graphs.