Cross-intersecting families of finite sets

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

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
Volume72
Issue number2
DOIs
Publication statusPublished - 1995

Fingerprint

Intersecting Family
Finite Set
Figure
Open Problems
Theorem
Family

ASJC Scopus subject areas

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

Cite this

Cross-intersecting families of finite sets. / Füredi, Z.

In: Journal of Combinatorial Theory, Series A, Vol. 72, No. 2, 1995, p. 332-339.

Research output: Contribution to journalArticle

@article{13f1f56242a54aef8fd41ef5ccaeb995,
title = "Cross-intersecting families of finite sets",
abstract = "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 Erd{\"o}s-Ko-Rado theorem for non-trivial intersecting families Several problems remain open.",
author = "Z. F{\"u}redi",
year = "1995",
doi = "10.1016/0097-3165(95)90072-1",
language = "English",
volume = "72",
pages = "332--339",
journal = "Journal of Combinatorial Theory - Series A",
issn = "0097-3165",
publisher = "Academic Press Inc.",
number = "2",

}

TY - JOUR

T1 - Cross-intersecting families of finite sets

AU - Füredi, Z.

PY - 1995

Y1 - 1995

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=26344452877&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=26344452877&partnerID=8YFLogxK

U2 - 10.1016/0097-3165(95)90072-1

DO - 10.1016/0097-3165(95)90072-1

M3 - Article

VL - 72

SP - 332

EP - 339

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

SN - 0097-3165

IS - 2

ER -