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|Paper IPM / M / 15577||
Given a family F of r-graphs, the Turán number of F for a given positive integer N, denoted by ex(N,F), is the maximum number of edges of an r-graph on N vertices that does not contain any member of F as a subgraph. For given r ≥ 3, a complete r-uniform Berge-hypergraph, denoted by Kn(r), is an r-uniform hypergraph of order n with the core sequence v1, v2, …,vn as the vertices and distinct edges eij, 1 ≤ i < j ≤ n, where every eij contains both vi and vj. Let F(r)n be the family of complete r-uniform Berge-hypergraphs of order n. We determine precisely ex(N,F(3)n) for n ≥ 13. We also find the extremal hypergraphs avoiding F(3)n.
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