3-uniform hypergraphs without a cycle of length five

Abstract

In this paper we show that the maximum number of hyperedges in a 3-uniform hypergraph on n vertices without a (Berge) cycle of length ve is less than (0:254+ o(1))n3=2, improving an estimate of Bollobas and Gy}ori. We obtain this result by showing that not many 3-paths can start from certain subgraphs of the shadow. Mathematics Subject Classications: 05C65, 05D99