A class of constructions for turán's (3, 4)-problem

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Let f(n) denote the minimal number of edges of a 3-uniform hypergraph G=(V, E) on n vertices such that for every quadruple Y ⊂V there exists Y ⊃e ∈E. Turán conjectured that f(3 k)=k(k-1)(2 k-1). We prove that if Turán's conjecture is correct then there exist at least 2 k-2 non-isomorphic extremal hypergraphs on 3 k vertices.

Original languageEnglish (US)
Pages (from-to)187-192
Number of pages6
Issue number2
StatePublished - Jun 1982
Externally publishedYes


  • AMS subject classification (1980): 05C35, 05C65

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics


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