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))(n−1k−1) edges if k≥r+1 and n is sufficiently large. Moreover, if r∈{3,4}, r|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 (n−1k−1), with equality only if all edges contain a specific vertex v. We also ask some related questions.