### Abstract

Following a conjecture of P. Erdös, we show that if F is a family of k-subsets of and n-set no two of which intersect in exactly l elements then for k ≥ 2l + 2 and n sufficiently large |F| ≤ (_{k - l - 1}
^{n - l - 1}) with equality holding if and only if F consists of all the k-sets containing a fixed (l + 1)-set. In general we show |F| ≤ d_{k}n^{max;{;l,k - l - 1};}, where d_{k} is a constant depending only on k. These results are special cases of more general theorems (Theorem 2.1-2.3).

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

Pages (from-to) | 160-176 |

Number of pages | 17 |

Journal | Journal of Combinatorial Theory, Series A |

Volume | 39 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1985 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Journal of Combinatorial Theory, Series A*,

*39*(2), 160-176. https://doi.org/10.1016/0097-3165(85)90035-4

**Forbidding just one intersection.** / Frankl, Peter; Füredi, Z.

Research output: Contribution to journal › Article

*Journal of Combinatorial Theory, Series A*, vol. 39, no. 2, pp. 160-176. https://doi.org/10.1016/0097-3165(85)90035-4

}

TY - JOUR

T1 - Forbidding just one intersection

AU - Frankl, Peter

AU - Füredi, Z.

PY - 1985

Y1 - 1985

N2 - Following a conjecture of P. Erdös, we show that if F is a family of k-subsets of and n-set no two of which intersect in exactly l elements then for k ≥ 2l + 2 and n sufficiently large |F| ≤ (k - l - 1 n - l - 1) with equality holding if and only if F consists of all the k-sets containing a fixed (l + 1)-set. In general we show |F| ≤ dknmax;{;l,k - l - 1};, where dk is a constant depending only on k. These results are special cases of more general theorems (Theorem 2.1-2.3).

AB - Following a conjecture of P. Erdös, we show that if F is a family of k-subsets of and n-set no two of which intersect in exactly l elements then for k ≥ 2l + 2 and n sufficiently large |F| ≤ (k - l - 1 n - l - 1) with equality holding if and only if F consists of all the k-sets containing a fixed (l + 1)-set. In general we show |F| ≤ dknmax;{;l,k - l - 1};, where dk is a constant depending only on k. These results are special cases of more general theorems (Theorem 2.1-2.3).

UR - http://www.scopus.com/inward/record.url?scp=0011476345&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0011476345&partnerID=8YFLogxK

U2 - 10.1016/0097-3165(85)90035-4

DO - 10.1016/0097-3165(85)90035-4

M3 - Article

AN - SCOPUS:0011476345

VL - 39

SP - 160

EP - 176

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

SN - 0097-3165

IS - 2

ER -