A lower bound on the multichromatic number of Kneser graphs

In 1976, S. Stahl formulated the conjecture on the multichromatic number of the Kneser graphs: For any positive integers m and n with m >= 2n, xnq+r(KGm,n) = mq vertical bar m - 2n vertical bar 2r, where 0 <= q and 0 < r <= n. It is well kown that xnq(KGm, n) = mq, moreover, Stahl's conjecture is equivalent to the claim that xnq+ 1(KGm, n) = mq vertical bar m -2n + 2. In [ 4] Stahl proved that the gap between xnq and xnq+ 1 is arbitrarily large if n is fixed and m is large enough. We shall prove here that xnq+ 1(KGm, n) >= mq + 3 for any positive integers m, n and q.