Extremal problems concerning Kneser graphs

P. Frankl, Z. Füredi

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

Let A and B be two intersecting families of k-subsets of an n-element set. It is proven that |A ∪ B| ≤ (k-1n-1) + (k-1n-1) holds for n> 1 2(3+ 5)k, and equality holds only if there exist two points a, b such that {a, b} ∩ F ≠ ∅ for all F ∈ A ∪ B. For n = 2k + o( k) an example showing that in this case max |A ∪ B| = (1-o(1))(kn) is given. This disproves an old conjecture of Erdös [7]. In the second part we deal with several generalizations of Kneser's conjecture.

Original languageEnglish
Pages (from-to)270-284
Number of pages15
JournalJournal of Combinatorial Theory. Series B
Volume40
Issue number3
DOIs
Publication statusPublished - 1986

Fingerprint

Kneser Graph
Extremal Problems
Intersecting Family
Disprove
Equality
Subset
Generalization

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Extremal problems concerning Kneser graphs. / Frankl, P.; Füredi, Z.

In: Journal of Combinatorial Theory. Series B, Vol. 40, No. 3, 1986, p. 270-284.

Research output: Contribution to journalArticle

@article{aa328e80386f44588e9bd6941c081c4c,
title = "Extremal problems concerning Kneser graphs",
abstract = "Let A and B be two intersecting families of k-subsets of an n-element set. It is proven that |A ∪ B| ≤ (k-1n-1) + (k-1n-1) holds for n> 1 2(3+ 5)k, and equality holds only if there exist two points a, b such that {a, b} ∩ F ≠ ∅ for all F ∈ A ∪ B. For n = 2k + o( k) an example showing that in this case max |A ∪ B| = (1-o(1))(kn) is given. This disproves an old conjecture of Erd{\"o}s [7]. In the second part we deal with several generalizations of Kneser's conjecture.",
author = "P. Frankl and Z. F{\"u}redi",
year = "1986",
doi = "10.1016/0095-8956(86)90084-5",
language = "English",
volume = "40",
pages = "270--284",
journal = "Journal of Combinatorial Theory. Series B",
issn = "0095-8956",
publisher = "Academic Press Inc.",
number = "3",

}

TY - JOUR

T1 - Extremal problems concerning Kneser graphs

AU - Frankl, P.

AU - Füredi, Z.

PY - 1986

Y1 - 1986

N2 - Let A and B be two intersecting families of k-subsets of an n-element set. It is proven that |A ∪ B| ≤ (k-1n-1) + (k-1n-1) holds for n> 1 2(3+ 5)k, and equality holds only if there exist two points a, b such that {a, b} ∩ F ≠ ∅ for all F ∈ A ∪ B. For n = 2k + o( k) an example showing that in this case max |A ∪ B| = (1-o(1))(kn) is given. This disproves an old conjecture of Erdös [7]. In the second part we deal with several generalizations of Kneser's conjecture.

AB - Let A and B be two intersecting families of k-subsets of an n-element set. It is proven that |A ∪ B| ≤ (k-1n-1) + (k-1n-1) holds for n> 1 2(3+ 5)k, and equality holds only if there exist two points a, b such that {a, b} ∩ F ≠ ∅ for all F ∈ A ∪ B. For n = 2k + o( k) an example showing that in this case max |A ∪ B| = (1-o(1))(kn) is given. This disproves an old conjecture of Erdös [7]. In the second part we deal with several generalizations of Kneser's conjecture.

UR - http://www.scopus.com/inward/record.url?scp=38249039814&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249039814&partnerID=8YFLogxK

U2 - 10.1016/0095-8956(86)90084-5

DO - 10.1016/0095-8956(86)90084-5

M3 - Article

AN - SCOPUS:38249039814

VL - 40

SP - 270

EP - 284

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

SN - 0095-8956

IS - 3

ER -