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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: $\lim_{n\to\infty} {t_3(n, 4)\over{n\choose 3}}\leq {3+\sqrt{17}\over 12}.$

##### MSC:
 05C65 Hypergraphs 05C35 Extremal problems in graph theory
##### Keywords:
Turán number; hypergraph
Full Text:
##### References:
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