A new short proof of the EKR theorem

Peter Frankl, Z. Füredi

Research output: Contribution to journalArticle

9 Citations (Scopus)

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 languageEnglish
Pages (from-to)1388-1390
Number of pages3
JournalJournal of Combinatorial Theory, Series A
Volume119
Issue number6
DOIs
Publication statusPublished - Aug 2012

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Intersecting Family
Subset
Erdös
Theorem
Family

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

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

In: Journal of Combinatorial Theory, Series A, Vol. 119, No. 6, 08.2012, p. 1388-1390.

Research output: Contribution to journalArticle

Frankl, Peter ; Füredi, Z. / A new short proof of the EKR theorem. In: Journal of Combinatorial Theory, Series A. 2012 ; Vol. 119, No. 6. pp. 1388-1390.
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