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Paper IPM / M / 15577  


Abstract:  
Given a family F of rgraphs, the Turán number of F for a given positive integer N, denoted by ex(N,F), is the maximum number of edges of an rgraph on N vertices that does not contain any member of F as a subgraph. For given r ≥ 3, a complete runiform Bergehypergraph, denoted by K_{n}^{(r)}, is an runiform hypergraph of order n with the core sequence v_{1}, v_{2}, …,v_{n} as the vertices and distinct edges e_{ij}, 1 ≤ i < j ≤ n, where every e_{ij} contains both v_{i} and v_{j}. Let F^{(r)}_{n} be the family of complete runiform Bergehypergraphs 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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