The multichromatic numbers of some Kneser graphs

The Kneser graph K(m,n) has the n-subsets of {1,2,…,m} as its vertices, two such vertices being adjacent whenever they are disjoint. The kth multichromatic number of the graph G is the least integer t such that the vertices of G can be assigned k-subsets of {1,2, …, t}, so that adjacent vertices of G receive disjoint sets. The values of Xk(K(m,n)) are computed for n = 2, 3 and bounded for n ⩾ 4.