Large Bd-free and union-free subfamilies

János Barát, Z. Füredi, Ida Kantor, Younjin Kim, Balázs Patkós

Research output: Contribution to journalArticle

Abstract

For a property Γ and a family of sets F, let f(F,Γ) be the size of the largest subfamily of F having property Γ. For a positive integer m, let f(m, Γ) be the minimum of f(F,Γ) over all families of size m. A family F is said to be Bd-free if it has no subfamily F'={FI:I⊆[d]} of 2d distinct sets such that for every I, J⊆[d], both FI∪FJ=FI∪J and FI∩FJ=FI∩J hold. A family F is a-union free if F1∪⋯∪Fa≠Fa+1 whenever F1,...,Fa+1 are distinct sets in F. We verify a conjecture of Erdos and Shelah that f(m, B2-free)=Θ(m2/3). We also obtain lower and upper bounds for f(m, Bd-free) and f(m, a-union free).

Original languageEnglish
Pages (from-to)101-104
Number of pages4
JournalElectronic Notes in Discrete Mathematics
Volume38
DOIs
Publication statusPublished - Dec 1 2011

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Keywords

  • B-free subfamilies
  • Extremal set theory
  • Union-free subfamilies

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Large Bd-free and union-free subfamilies. / Barát, János; Füredi, Z.; Kantor, Ida; Kim, Younjin; Patkós, Balázs.

In: Electronic Notes in Discrete Mathematics, Vol. 38, 01.12.2011, p. 101-104.

Research output: Contribution to journalArticle

Barát, János ; Füredi, Z. ; Kantor, Ida ; Kim, Younjin ; Patkós, Balázs. / Large Bd-free and union-free subfamilies. In: Electronic Notes in Discrete Mathematics. 2011 ; Vol. 38. pp. 101-104.
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