Abstract
Letf(n) denote the minimal number of edges of a 3-uniform hypergraphG=(V, E) onn vertices such that for every quadrupleY ⊂V there existsY ⊃e ∈E. 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
W. G. Brown, On an open problem of Paul Turán concerning 3-graphs,Studies in Pure Mathematics (to appear).
P. Turán, Research problems,Magyar Tud. Akad. Mat. Kut. Int. Közl. 6 (1961), 417–423.