Turan Problems for Berge-(k, p)-Fan Hypergraph

Let F be a graph. A hypergraph H is Berge-F if there is a bijection f : E(F) -> E(H) such that e subset of f(e) for every e is an element of E(F). A hypergraph is Berge-F-free if it does not contain a subhypergraph isomorphic to a Berge-F hypergraph. The authors denote the maximum number of hyperedges in an n-vertex r-uniform Berge-F-free hypergraph by ex(r)(n, Berge-F). A (k, p)-fan, denoted by F-k,F-p, is a graph on k(p - 1) +1 vertices consisting of k cliques with p vertices that intersect in exactly one common vertex. In this paper they determine the bounds of ex(r)(n, Berge-F) when F is a (k, p)-fan for k >= 2, p >= 3 and r >= 3.