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Asymptotic solution of a Turán-type problem. (English) Zbl 0724.05070
Let f(n,k) be the maximum number of edges in a 2k-uniform hypergraph on n vertices which does not contain edges of the form $$A\cup B$$, $$A\cup C$$, $$B\cup C$$ where A, B and C are disjoint k-element sets. The following theorem (related to a problem of B. Bollabás) is proved: $(\frac{1}{2}+\frac{c}{n^ 2})/\left( \begin{matrix} n\\ 2k\end{matrix} \right)<f(n,k)<(\frac{1}{2}+\frac{2k}{n-4k})\left( \begin{matrix} n\\ 2k\end{matrix} \right),$ where $$c=c(k)>0$$ is a constant. Finally the structure of an extremal hypergraph is conjectured.
Reviewer: K.Engel (Rostock)

MSC:
 05D05 Extremal set theory 05C35 Extremal problems in graph theory 05C65 Hypergraphs
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References:
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