## Abstract

Let F be a graph. We say that a hypergraph H is a Berge-F if there is a bijection f:E(F)→E(H) such that e⊆f(e) for every e∈E(F). Note that Berge-F actually denotes a class of hypergraphs. The maximum number of edges in an n-vertex r-graph with no subhypergraph isomorphic to any Berge-F is denoted ex _{r} (n,Berge-F). In this paper, we investigate the case when F=K _{s,t} and establish an upper-bound when r≥3, and a lower-bound when r=4 and t is large enough compared to s. Additionally, we prove a counting result for r-graphs of girth five that complements the asymptotic formula ex _{3} (n,Berge-{C _{2} ,C _{3} ,C _{4} })=[Formula presented]n ^{3∕2} +o(n ^{3∕2} ) of Lazebnik and Verstraëte (2003).

Original language | English |
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Pages (from-to) | 1553-1563 |

Number of pages | 11 |

Journal | Discrete Mathematics |

Volume | 342 |

Issue number | 6 |

DOIs | |

State | Published - Jun 2019 |

## Keywords

- Berge-hypergraph
- Turán number
- extremal problems