On Hypergraphs of Girth Five

  title={On Hypergraphs of Girth Five},
  author={Felix Lazebnik and Jacques Verstra{\"e}te},
  journal={Electr. J. Comb.},
In this paper, we study r-uniform hypergraphs H without cycles of length less than five, employing the definition of a hypergraph cycle due to Berge. In particular, for r = 3, we show that if H has n vertices and a maximum number of edges, then |H| = 1 6 n + o(n). This also asymptotically determines the generalized Turán number T3(n, 8, 4). Some results are based on our bounds for the maximum size of Sidon-type sets in Zn. 1 Definitions In this paper, a hypergraph H is a family of distinct… CONTINUE READING
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