A new short proof of the EKR theorem

Peter Frankl, Zoltán Füredi

Research output: Contribution to journalArticle

13 Citations (Scopus)


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
Issue number6
Publication statusPublished - Aug 1 2012



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

ASJC Scopus subject areas

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

Cite this