Saturating Sperner Families

Dániel Gerbner, Balázs Keszegh, Nathan Lemons, Cory Palmer, Dömötör Pálvölgyi, Balázs Patkós

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


A family F ⊆ 2[n] saturates the monotone decreasing property P if F satisfies P and one cannot add any set to F such that property P is still satisfied by the resulting family. We address the problem of finding the minimum size of a family saturating the k-Sperner property and the minimum size of a family that saturates the Sperner property and that consists only of l-sets and (l + 1)-sets.

Original languageEnglish
Pages (from-to)1355-1364
Number of pages10
JournalGraphs and Combinatorics
Issue number5
StatePublished - Sep 2013


  • Extremal set theory
  • Saturation
  • Sperner property

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