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An upper bound for the Turán number \(t_3(n,4)\). (English) Zbl 0946.05063
It is proved that the smallest number \(t_3(n,4)\) such that every 3-uniform hypergraph on \(n\) vertices with more than \(t_3(n,4)\) edges necessarily contains a complete subgraph with 4 vertices, satisfies the following upper bound: \[ \lim_{n\to\infty} {t_3(n, 4)\over{n\choose 3}}\leq {3+\sqrt{17}\over 12}. \]

05C65 Hypergraphs
05C35 Extremal problems in graph theory
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