# Non-trivial intersecting families

P. Frankl, Z. Füredi

Research output: Contribution to journalArticle

37 Citations (Scopus)

### 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 150-153 4 Journal of Combinatorial Theory, Series A 41 1 https://doi.org/10.1016/0097-3165(86)90121-4 Published - 1986

### Fingerprint

Intersecting Family
Subset
Theorem
Disjoint
Family

### ASJC Scopus subject areas

• Discrete Mathematics and Combinatorics
• Theoretical Computer Science

### Cite this

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

In: Journal of Combinatorial Theory, Series A, Vol. 41, No. 1, 1986, p. 150-153.

Research output: Contribution to journalArticle

title = "Non-trivial intersecting families",
abstract = "The Erd{\"o}s-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 = {\O} 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.",
author = "P. Frankl and Z. F{\"u}redi",
year = "1986",
doi = "10.1016/0097-3165(86)90121-4",
language = "English",
volume = "41",
pages = "150--153",
journal = "Journal of Combinatorial Theory - Series A",
issn = "0097-3165",
number = "1",

}

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.

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

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

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VL - 41

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EP - 153

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

SN - 0097-3165

IS - 1

ER -