### Abstract

Fifteen years ago Chvátal conjectured that if F is a family of k subsets of an n-set, |F|>( n-1 k-1), d is an arbitrary integer with d ≤ k - 1 and (d + 1) k ≤ dn, then there exist d + 1 sets in F with empty intersection such that the intersection of any d of them is non-empty. The validity of this conjecture is established for n ≥ n_{0}(k), in a more general framework. Another problem which is solved asymptotically is when the excluded configuration is a fixed sunflower.

Original language | English |
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Pages (from-to) | 226-262 |

Number of pages | 37 |

Journal | Journal of Combinatorial Theory, Series A |

Volume | 45 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jul 1987 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

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## Cite this

Frankl, P., & Füredi, Z. (1987). Exact solution of some Turán-type problems.

*Journal of Combinatorial Theory, Series A*,*45*(2), 226-262. https://doi.org/10.1016/0097-3165(87)90016-1