The turán number of berge-K 4 in triple systems

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2 Citations (Scopus)


A Berge-K 4 in a triple system is a configuration with four vertices v1, v2, v3, v4 and six distinct triples { eij: 1 ≤ i < j ≤ 4} such that { vi, vj} ⊂ eij for every 1 ≤ i < j ≤ 4. We denote by B the set of Berge-K 4 configurations. A triple system is B-free if it does not contain any member of B. We prove that the maximum number of triples in a B -free triple system on n > 6 points is obtained by the balanced complete 3-partite triple system: all triples { abc : a ∈ A, b ∈ B, c ∈ C} where A,B,C is a partition of n points with ⌊ n/3⌋ = | A| ≤ |B| ≤ | C| = ⌈ n/3⌉.

Original languageEnglish
Pages (from-to)383-392
Number of pages10
JournalSIAM Journal on Discrete Mathematics
Issue number1
Publication statusPublished - Jan 1 2019


  • Berge-G hypergraphs
  • Triple system
  • Turán number

ASJC Scopus subject areas

  • Mathematics(all)

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