Two-regular subgraphs of odd-uniform hypergraphs

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−1k−1)+⌊n−1k⌋, 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 Verstraëte.