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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)

05D05 Extremal set theory
05C35 Extremal problems in graph theory
05C65 Hypergraphs
Full Text: DOI
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