### Abstract

The exact bound in the Erdo{combining double acute accent}s-Ko-Rado theorem is known [F, W]. It states that if n ≥ (t + 1)(k - t + 1), and F is a t-intersecting family of k-sets of an n-set (|F ∩ F′| ≥ t for all F, F′ ∈ F),then |F≤( n-1 k-1). Define A_{r} = {F ⊂ {1, 2, ..., n} : |F| = k, |F ∩ {1, 2, ..., t + 2r}| ≥ t + r}. Here it is proved that for n>c t log(t+1) (k - t + 1) one has |F| ≤ max_{r} |A_{r}|.

Original language | English |
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Pages (from-to) | 182-194 |

Number of pages | 13 |

Journal | Journal of Combinatorial Theory, Series A |

Volume | 56 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1991 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

**Beyond the Erdo{combining double acute accent}s-Ko-Rado theorem.** / Frankl, Peter; Füredi, Z.

Research output: Contribution to journal › Article

*Journal of Combinatorial Theory, Series A*, vol. 56, no. 2, pp. 182-194. https://doi.org/10.1016/0097-3165(91)90031-B

}

TY - JOUR

T1 - Beyond the Erdo{combining double acute accent}s-Ko-Rado theorem

AU - Frankl, Peter

AU - Füredi, Z.

PY - 1991

Y1 - 1991

N2 - The exact bound in the Erdo{combining double acute accent}s-Ko-Rado theorem is known [F, W]. It states that if n ≥ (t + 1)(k - t + 1), and F is a t-intersecting family of k-sets of an n-set (|F ∩ F′| ≥ t for all F, F′ ∈ F),then |F≤( n-1 k-1). Define Ar = {F ⊂ {1, 2, ..., n} : |F| = k, |F ∩ {1, 2, ..., t + 2r}| ≥ t + r}. Here it is proved that for n>c t log(t+1) (k - t + 1) one has |F| ≤ maxr |Ar|.

AB - The exact bound in the Erdo{combining double acute accent}s-Ko-Rado theorem is known [F, W]. It states that if n ≥ (t + 1)(k - t + 1), and F is a t-intersecting family of k-sets of an n-set (|F ∩ F′| ≥ t for all F, F′ ∈ F),then |F≤( n-1 k-1). Define Ar = {F ⊂ {1, 2, ..., n} : |F| = k, |F ∩ {1, 2, ..., t + 2r}| ≥ t + r}. Here it is proved that for n>c t log(t+1) (k - t + 1) one has |F| ≤ maxr |Ar|.

UR - http://www.scopus.com/inward/record.url?scp=44949281931&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=44949281931&partnerID=8YFLogxK

U2 - 10.1016/0097-3165(91)90031-B

DO - 10.1016/0097-3165(91)90031-B

M3 - Article

AN - SCOPUS:44949281931

VL - 56

SP - 182

EP - 194

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

SN - 0097-3165

IS - 2

ER -