Maximum hypergraphs without regular subgraphs

Abstract

We show that an n-vertex hypergraph with no r-regular subgraphs has at most 2n−1 + r− 2 edges. We conjecture that if n > r, then every n-vertex hypergraph with no r-regular subgraphs having the maximum number of edges contains a full star, that is, 2n−1 distinct edges containing a given vertex. We prove this conjecture for n ≥ 425. The condition that n > r cannot be weakened.