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

Abstract

Letf(n) denote the minimal number of edges of a 3-uniform hypergraphG=(V, E) onn vertices such that for every quadrupleYV there existsYeE. Turán conjectured thatf(3k)=k(k−1)(2k−1). We prove that if Turán’s conjecture is correct then there exist at least 2k−2 non-isomorphic extremal hypergraphs on 3k vertices.

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References

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    W. G. Brown, On an open problem of Paul Turán concerning 3-graphs,Studies in Pure Mathematics (to appear).

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    P. Turán, Research problems,Magyar Tud. Akad. Mat. Kut. Int. Közl. 6 (1961), 417–423.

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Kostochka, A.V. A class of constructions for turán’s (3, 4)-problem. Combinatorica 2, 187–192 (1982). https://doi.org/10.1007/BF02579317

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AMS subject classification (1980)

  • 05 C 35
  • 05 C 65