### Abstract

A Berge-K
_{4}
in a triple system is a configuration with four vertices v1, v2, v3, v4 and six distinct triples { eij: 1 ≤ i < j ≤ 4} such that { vi, vj} ⊂ eij for every 1 ≤ i < j ≤ 4. We denote by B the set of Berge-K
_{4}
configurations. A triple system is B-free if it does not contain any member of B. We prove that the maximum number of triples in a B -free triple system on n > 6 points is obtained by the balanced complete 3-partite triple system: all triples { abc : a ∈ A, b ∈ B, c ∈ C} where A,B,C is a partition of n points with ⌊ n/3⌋ = | A| ≤ |B| ≤ | C| = ⌈ n/3⌉.

Original language | English |
---|---|

Pages (from-to) | 383-392 |

Number of pages | 10 |

Journal | SIAM Journal on Discrete Mathematics |

Volume | 33 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2019 |

### Keywords

- Berge-G hypergraphs
- Triple system
- Turán number

### ASJC Scopus subject areas

- Mathematics(all)