On unavoidable hypergraphs

A r-uniform hypergraph H (or a r-graph, for short) is a collection E = E(H) of r-element subsets (called edges) of a set V = V(H) (called vertices). We say a r-graph H is (n, e)-unavoidable if every r-graph with n vertices and e edges must contain H. In this paper we investigate the largest possible number of edges in an (n, e)-unavoidable 3-graph for fixed n and e. We also study the structure of such unavoidable 3-graphs.