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 languageEnglish
Pages (from-to)150-153
Number of pages4
JournalJournal of Combinatorial Theory, Series A
Volume41
Issue number1
DOIs
Publication statusPublished - 1986

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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

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