### Abstract

It is proved that A is a family of a-element sets and B is a family of b-element sets on the common undelying set [n], and A ∩ B ≠ ∅ for all A ∈ A, B ∈ B (i.e., cross-intersecting), and n ≥ a + b, {A figure is presented}, and {A figure is presented} then there exists an element xε{lunate}[n] such that it belongs to all members of A and B. This is an extension of a result of Hilton and Milner who generalized the Erdös-Ko-Rado theorem for non-trivial intersecting families Several problems remain open.

Original language | English |
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Pages (from-to) | 332-339 |

Number of pages | 8 |

Journal | Journal of Combinatorial Theory, Series A |

Volume | 72 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1995 |

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### ASJC Scopus subject areas

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

### Cite this

**Cross-intersecting families of finite sets.** / Füredi, Z.

Research output: Contribution to journal › Article

*Journal of Combinatorial Theory, Series A*, vol. 72, no. 2, pp. 332-339. https://doi.org/10.1016/0097-3165(95)90072-1

}

TY - JOUR

T1 - Cross-intersecting families of finite sets

AU - Füredi, Z.

PY - 1995

Y1 - 1995

N2 - It is proved that A is a family of a-element sets and B is a family of b-element sets on the common undelying set [n], and A ∩ B ≠ ∅ for all A ∈ A, B ∈ B (i.e., cross-intersecting), and n ≥ a + b, {A figure is presented}, and {A figure is presented} then there exists an element xε{lunate}[n] such that it belongs to all members of A and B. This is an extension of a result of Hilton and Milner who generalized the Erdös-Ko-Rado theorem for non-trivial intersecting families Several problems remain open.

AB - It is proved that A is a family of a-element sets and B is a family of b-element sets on the common undelying set [n], and A ∩ B ≠ ∅ for all A ∈ A, B ∈ B (i.e., cross-intersecting), and n ≥ a + b, {A figure is presented}, and {A figure is presented} then there exists an element xε{lunate}[n] such that it belongs to all members of A and B. This is an extension of a result of Hilton and Milner who generalized the Erdös-Ko-Rado theorem for non-trivial intersecting families Several problems remain open.

UR - http://www.scopus.com/inward/record.url?scp=26344452877&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=26344452877&partnerID=8YFLogxK

U2 - 10.1016/0097-3165(95)90072-1

DO - 10.1016/0097-3165(95)90072-1

M3 - Article

VL - 72

SP - 332

EP - 339

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

SN - 0097-3165

IS - 2

ER -