On 2-connected hypergraphs with no long cycles

Zoltán Füredi, Alexandr Kostochka, Ruth Luo

Research output: Contribution to journalArticlepeer-review

Abstract

We give an upper bound for the maximum number of edges in an n-vertex 2-connected r-uniform hypergraph with no Berge cycle of length k or greater, where n ≥ k ≥ 4r ≥ 12. For n large with respect to r and k, this bound is sharp and is significantly stronger than the bound without restrictions on connectivity. It turned out that it is simpler to prove the bound for the broader class of Sperner families where the size of each set is at most r. For such families, our bound is sharp for all n ≥ k ≥ r ≥ 3.

Original languageEnglish (US)
Article numberP4.31
JournalElectronic Journal of Combinatorics
Volume26
Issue number4
DOIs
StatePublished - 2019

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics

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