Edge-colorings of uniform hypergraphs avoiding monochromatic matchings

For positive integers k, l and r, and an r-uniform hypergraph H, let c(k,l,r) (H) be the number of k-colorings of the set of hyperedges of H with no l independent hyperedges of the same color. Let H-n,H-r denote the set of all n-vertex r-uniform hypergraphs and consider the function c(k,l,r) (n) = max {c(k,l,r)(H): H epsilon H-n,H-r}, the maximum of C-k,C-l,C-r (H) over all r-uniform hypergraphs H on n vertices. In this paper, we determine, for all fixed values of r, k and l, and large n, the r-uniform n-vertex hypergraphs H with C-k,C-l,C-r (n) = C-k,C-l,C-r (H). (C) 2014 Elsevier B.V. All rights reserved.