Turán densities of some hypergraphs related to Kk k+1

József Balogh, Tom Bohman, Béla Bollobás, Yi Zhao

Research output: Contribution to journalArticlepeer-review


Let Bi(k) be the k-uniform hypergraph whose vertex set is of the form S U T, where |S| = i, |T| = k - 1, and S∩T = φ, and whose edges are the k-subsets of S∪T that contain either S or T. We derive upper and lower bounds for the Turan density of Bi (k) that are close to each other as k → ∞. We also obtain asymptotically tight bounds for the Turan density of several other infinite families of hypergraphs. The constructions that imply the lower bounds are derived from elementary number theory by probabilistic arguments, and the upper bounds follow from some results of de Caen, Sidorenko, and Keevash.

Original languageEnglish (US)
Pages (from-to)1609-1617
Number of pages9
JournalSIAM Journal on Discrete Mathematics
Issue number4
StatePublished - 2012


  • Extremal problem
  • Hypergraph
  • Turán density

ASJC Scopus subject areas

  • Mathematics(all)


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