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.