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{\bf Dhruv Mubayi }
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{\bf On Hypergraphs with Every Four Points Spanning at Most Two Triples}
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Let ${\cal F}$ be a triple system on an $n$ element set.  Suppose that
${\cal F}$ contains more than $(1/3-\epsilon){n\choose 3}$ triples, where
$\epsilon>10^{-6}$ is explicitly defined and $n$ is sufficiently
large.  Then there is a set of four points containing at least three
triples of ${\cal F}$. This improves previous bounds of de Caen
and Matthias.

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