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The Turán numbers of two kinds of Berge hypergraphs

The Turán numbers of two kinds of Berge hypergraphs

Let F be a graph. A hypergraph mathcalHis called a Berge-F if there is a bijection phi: E(F)to E(mathcalH such that e⊆ phi(e) for each e∈ E(F). We say that the hypergraph mathcalHis Berge-F-free if there is no sub-hypergraph of mathcalHisomorphic to any Berge-F. The maximum number of edges, denoted …