On Hypergraphs with Every Four Points Spanning at Most Two Triples

@article{Mubayi2003OnHW,
  title={On Hypergraphs with Every Four Points Spanning at Most Two Triples},
  author={Dhruv Mubayi},
  journal={Electr. J. Comb.},
  year={2003},
  volume={10}
}
Let F be a triple system on an n element set. Suppose that F contains more than (1/3 − ) ( n 3 ) triples, where > 10−6 is explicitly defined and n is sufficiently large. Then there is a set of four points containing at least three triples of F . This improves previous bounds of de Caen [1] and Matthias [7] . Given an r-graph F , the Turán number ex(n,F) is the maximum number of edges in an n vertex r-graph containing no member of F . The Turán density π(F) = limn→∞ ex(n,F) (nr) . When π(F) 6= 0… CONTINUE READING