Regular subgraphs of uniform hypergraphs

Abstract

We prove that for every integer r >= 2, an n-vertex k-uniform hypergraph H containing no r-regular subgraphs has at most (1 + o(1)) [GRAPHICS] edges if k >= r + 1 and n is sufficiently large. Moreover, if r is an element of {3, 4}, r vertical bar k and k, n are both sufficiently large, then the maximum number of edges in an n-vertex k-uniform hypergraph containing no r-regular subgraphs is exactly [GRAPHICS] , with equality only if all edges contain a specific vertex v. We also ask some related questions. (C) 2016 Elsevier Inc. All rights reserved.