Almost Cross-Intersecting and Almost Cross-Sperner Pairs of Families of Sets

Dániel Gerbner, Nathan Lemons, Cory Palmer, Dömötör Pálvölgyi, Balázs Patkós, Vajk Szécsi

Research output: Contribution to journalArticlepeer-review

Abstract

For a set G and a family of sets F let DF(G) = {F ∈ F: F ∩ G= ∅} SF(G) ={F ∈ F: F ⊆ or G ⊆ F} We say that a family is l-almost intersecting, (≤ l)-almost intersecting, l-almost Sperner, (≤ l)-almost Sperner if {pipe}DF(F){pipe}≤l, {pipe}SF(F){pipe} = {pipe}SF(F){pipe}≤l (respectively) for all F ∈ F. We consider the problem of finding the largest possible family for each of the above properties. We also address the analogous generalization of cross-intersecting and cross-Sperner families.

Original languageEnglish
Pages (from-to)489-498
Number of pages10
JournalGraphs and Combinatorics
Volume29
Issue number3
DOIs
StatePublished - May 2013

Keywords

  • Extremalset systems
  • Intersecting families
  • Pairs of families
  • Sperner families

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