Coloring uniform hypergraphs with few colors

Abstract

Abstract Let m ( r , k ) denote the minimum number of edges in an r ‐uniform hypergraph that is not k ‐colorable. We give a new lower bound on m ( r , k ) for fixed k and large r . Namely, we prove that if k ≥ 2 n , then m ( r , k ) ≥ ϵ( k ) k r ( r /ln r ) n /( n +1) . © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2004