Füredi Zoltán (Renyi Institute): A Turan type problem for triple-systems

Let F be a triple system of 4 members consisting of three disjoint edges and the fourth one meeting each in a singleton. We prove the following conjecture of Gyarfas (in a stronger form). If  H  is a 3-uniform hypergraph with n vertices, F-free, and  n is sufficiently large then |H| \leq (n-2)^2. Here equality holds only if H consists of all {n-1 \choose 2} + {n-2\choose 2} triples meeting two given vertices. Our main aim is presenting the proof ideas, but we also mention related results and problems.