The chromatic numbers of random hypergraphs

For a pair of integers 1≤γ<r, the γ-chromatic number of an r-uniform hypergraph H=(V, E) is the minimal k, for which there exists a partition of V into subsets T₁,…,T_k such that |e∩T_i|≤γ for every e∈E. In this paper we determine the asymptotic behavior of the γ-chromatic number of the random r-uniform hypergraph H_r(n, p) for all possible values of γ and for all values of p down to p=Θ(n^−r+1). © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 12: 381–403, 1998