On the maximal number of edges in a homogeneous hypergraph not containing prohibited subgraphs (Q1123216)

The author proves that the maximal number of edges of a 4-uniform hypergraph with n vertices without two edges whose symmetric difference is contained in a third is equal to \(\lfloor n/4\rfloor \lfloor (n+1)/4\rfloor \lfloor (n+2)/4\rfloor \lfloor (n+3)/4\rfloor\) and that the extremal hypergraph is unique up to isomorphism. This settles a conjecture of \textit{B. Bollobás}, who solved the corresponding problem for 3-uniform hypergraphs [Discrete Math. 8, 21-24 (1974; Zbl 0291.05114)].