Extremal results for Berge-hypergraphs

Joint work with Cory Palmer Let G be a graph and \mathcal{H} be a hypergraph both on the same vertex set. We say that \mathcal{H} is a Berge-G if there is a bijection f : E(G) -> E(\mathcal{H}) such that for e \in E(G) we have e \subset f(e). This generalizes the established definitions of «Berge path» and «Berge cycle» to general graphs. For a fixed graph G we examine the maximum possible size (i.e. the sum of the cardinality of each edge) of a hypergraph with no Berge-G as a subhypergraph. In the present talk we prove general bounds for this maximum when G is an arbitrary graph. We also consider the specific case when G is a complete bipartite graph and prove an analogue of the Kővári-Sós-Turán theorem.