Two-regular subgraphs of odd-uniform hypergraphs

Abstract

Let k >= 3 be an odd integer and let n be a sufficiently large integer. We prove that the maximum number of edges in an n-vertex k-uniform hypergraph containing no 2-regular subgraphs is ((n-1)(k-1)) + left perpendicular n-1/k right perpendicular, and the equality holds if and only if H is a full k-star with center v together with a maximal matching omitting v. This verifies a conjecture of Mubayi and Verstraete. (C) 2017 Elsevier Inc. All rights reserved.