Geodesic
On hypergraphs with every four points spanning at most two triples
The electronic journal of combinatorics, Tome 10 (2003)
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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.
DOI : 10.37236/1750
Classification : 05C65, 05C35, 05D05 
@article{10_37236_1750,
     author = {Dhruv Mubayi},
     title = {On hypergraphs with every four points spanning at most two triples},
     journal = {The electronic journal of combinatorics},
     year = {2003},
     volume = {10},
     doi = {10.37236/1750},
     zbl = {1023.05105},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1750/}
}
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Dhruv Mubayi. On hypergraphs with every four points spanning at most two triples. The electronic journal of combinatorics, Tome 10 (2003). doi: 10.37236/1750

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