Abstract
Saul Stahl defined the s-tuple coloring of a graph G and formulated a conjecture on the multichromatic numbers of the Kneser graph KGm,n. The conjecture was completely proved for graph parameters n=2,3, and m=2n+1 by Stahl, and in specially for m=10 and n=4 by Kincses et al. Furthermore we know that the conjecture is true if s=qn. In this paper we present a new lower bound for the multichromatic numbers of KGm,n, which is sharp for graph parameters 2n<m<3n and cases qn−nm−2n<s<qn. So we confirm Stahl’s conjecture in these new cases.
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