### Abstract

A family F is intersecting if F∩F ^{'}≠θ whenever F,F'∈F. Erdos, Ko, and Rado (1961) [6] showed that(1)|F|≤(n-1k-1) holds for an intersecting family of k-subsets of [n]:={1, 2, 3,, n}, n≥2k. For n>2k the only extremal family consists of all k-subsets containing a fixed element. Here a new proof is presented by using the Katona's shadow theorem for t-intersecting families.

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

Pages (from-to) | 1388-1390 |

Number of pages | 3 |

Journal | Journal of Combinatorial Theory, Series A |

Volume | 119 |

Issue number | 6 |

DOIs | |

Publication status | Published - Aug 2012 |

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### Keywords

- Erdos-Ko-Rado
- Generalized characteristic vectors
- Intersecting hypergraphs
- Multilinear polynomials
- Shadows

### ASJC Scopus subject areas

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

### Cite this

*Journal of Combinatorial Theory, Series A*,

*119*(6), 1388-1390. https://doi.org/10.1016/j.jcta.2012.03.012

**A new short proof of the EKR theorem.** / Frankl, Peter; Füredi, Z.

Research output: Contribution to journal › Article

*Journal of Combinatorial Theory, Series A*, vol. 119, no. 6, pp. 1388-1390. https://doi.org/10.1016/j.jcta.2012.03.012

}

TY - JOUR

T1 - A new short proof of the EKR theorem

AU - Frankl, Peter

AU - Füredi, Z.

PY - 2012/8

Y1 - 2012/8

N2 - A family F is intersecting if F∩F '≠θ whenever F,F'∈F. Erdos, Ko, and Rado (1961) [6] showed that(1)|F|≤(n-1k-1) holds for an intersecting family of k-subsets of [n]:={1, 2, 3,, n}, n≥2k. For n>2k the only extremal family consists of all k-subsets containing a fixed element. Here a new proof is presented by using the Katona's shadow theorem for t-intersecting families.

AB - A family F is intersecting if F∩F '≠θ whenever F,F'∈F. Erdos, Ko, and Rado (1961) [6] showed that(1)|F|≤(n-1k-1) holds for an intersecting family of k-subsets of [n]:={1, 2, 3,, n}, n≥2k. For n>2k the only extremal family consists of all k-subsets containing a fixed element. Here a new proof is presented by using the Katona's shadow theorem for t-intersecting families.

KW - Erdos-Ko-Rado

KW - Generalized characteristic vectors

KW - Intersecting hypergraphs

KW - Multilinear polynomials

KW - Shadows

UR - http://www.scopus.com/inward/record.url?scp=84859046580&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84859046580&partnerID=8YFLogxK

U2 - 10.1016/j.jcta.2012.03.012

DO - 10.1016/j.jcta.2012.03.012

M3 - Article

VL - 119

SP - 1388

EP - 1390

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

SN - 0097-3165

IS - 6

ER -