Even cycles in hypergraphs

A cycle in a hypergraph is an alternating cyclic sequence A 0 , v 0 , A 1 , v 1 , … , A k - 1 , v k - 1 , A 0 of distinct edges A i and vertices v i such that v i ∈ A i ∩ A i + 1 for all i modulo k. In this paper, we determine the maximum number of edges in hypergraphs on n vertices containing no even cycles.