Two-regular subgraphs of hypergraphs

We prove that the maximum number of edges in a k-uniform hypergraph on n vertices containing no 2-regular subhypergraph is ( n − 1 k − 1 ) if k ⩾ 4 is even and n is sufficiently large. Equality holds only if all edges contain a specific vertex v. For odd k we conjecture that this maximum is ( n − 1 k − 1 ) + ⌊ n − 1 k ⌋ , with equality only for the hypergraph described above plus a maximum matching omitting v.