Hypergraph based Berge hypergraphs

Abstract

Fix a hypergraph F. A hypergraph H is called a Berge copy of F or Berge-F if we can choose a subset of each hyperedge of H to obtain a copy of F. A hypergraph H is Berge-F-free if it does not contain a subhypergraph which is Berge copy of F. This is a generalization of the usual, graph based Berge hypergraphs, where F is a graph.In this paper, we study extremal properties of hypergraph based Berge hypergraphs and generalize several results from the graph based setting. In particular, we show