### Abstract

The Erdös-Ko-Rado theorem states that if F is a family of k-subsets of an n-set no two of which are disjoint, n ≥ 2k, then |F| ≤ n-1 k-1 holds. Taking all k-subsets through a point shows that this bound is best possible. Hilton and Milner showed that if ∩ F = Ø then |F|≤ n-1 k-1- n-k-1 k-1+1 holds and this is best possible. In this note a new, short proof of this theorem is given.

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

Pages (from-to) | 150-153 |

Number of pages | 4 |

Journal | Journal of Combinatorial Theory, Series A |

Volume | 41 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1986 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Journal of Combinatorial Theory, Series A*,

*41*(1), 150-153. https://doi.org/10.1016/0097-3165(86)90121-4

**Non-trivial intersecting families.** / Frankl, P.; Füredi, Z.

Research output: Contribution to journal › Article

*Journal of Combinatorial Theory, Series A*, vol. 41, no. 1, pp. 150-153. https://doi.org/10.1016/0097-3165(86)90121-4

}

TY - JOUR

T1 - Non-trivial intersecting families

AU - Frankl, P.

AU - Füredi, Z.

PY - 1986

Y1 - 1986

N2 - The Erdös-Ko-Rado theorem states that if F is a family of k-subsets of an n-set no two of which are disjoint, n ≥ 2k, then |F| ≤ n-1 k-1 holds. Taking all k-subsets through a point shows that this bound is best possible. Hilton and Milner showed that if ∩ F = Ø then |F|≤ n-1 k-1- n-k-1 k-1+1 holds and this is best possible. In this note a new, short proof of this theorem is given.

AB - The Erdös-Ko-Rado theorem states that if F is a family of k-subsets of an n-set no two of which are disjoint, n ≥ 2k, then |F| ≤ n-1 k-1 holds. Taking all k-subsets through a point shows that this bound is best possible. Hilton and Milner showed that if ∩ F = Ø then |F|≤ n-1 k-1- n-k-1 k-1+1 holds and this is best possible. In this note a new, short proof of this theorem is given.

UR - http://www.scopus.com/inward/record.url?scp=38249042944&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249042944&partnerID=8YFLogxK

U2 - 10.1016/0097-3165(86)90121-4

DO - 10.1016/0097-3165(86)90121-4

M3 - Article

AN - SCOPUS:38249042944

VL - 41

SP - 150

EP - 153

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

SN - 0097-3165

IS - 1

ER -