Two-regular subgraphs of odd-uniform hypergraphs

Let $kge 3$ 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 $binom{n-1}{k-1} + lfloorfrac{n-1}{k} rfloor$, 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 Verstra{e}te.