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Extremal problems for triple systems. (English) Zbl 0817.05015
Summary: Turán-type problems for several triple systems arising from \((k,k- 2)\)- configurations [i.e. \((k- 2)\) triples on \(k\) vertices] are considered. It is shown that every Steiner triple system contains a \((k,k- 2)\)- configuration for some \(k< c\log n/\log\log n\). Moreover, the Turán numbers of \((k,k- 2)\)-trees are determined asymptotically to be \(((k- 3)/3)\cdot(\begin{smallmatrix} n\\ 2\end{smallmatrix})(1- o(1))\). Finally, anti- Pasch hypergraphs avoiding \((5,3)\)- and \((6,4)\)-configurations are considered.

MSC:
05B07 Triple systems
51E10 Steiner systems in finite geometry
05C65 Hypergraphs
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