Cross-intersecting families of finite sets

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5 Citations (Scopus)


It is proved that A is a family of a-element sets and B is a family of b-element sets on the common undelying set [n], and A ∩ B ≠ ∅ for all A ∈ A, B ∈ B (i.e., cross-intersecting), and n ≥ a + b, {A figure is presented}, and {A figure is presented} then there exists an element xε{lunate}[n] such that it belongs to all members of A and B. This is an extension of a result of Hilton and Milner who generalized the Erdös-Ko-Rado theorem for non-trivial intersecting families Several problems remain open.

Original languageEnglish
Pages (from-to)332-339
Number of pages8
JournalJournal of Combinatorial Theory, Series A
Issue number2
Publication statusPublished - Nov 1995

ASJC Scopus subject areas

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

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