On 3-uniform hypergraphs without a cycle of a given length


Furedi Z., ÖZKAHYA L.

DISCRETE APPLIED MATHEMATICS, vol.216, pp.582-588, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 216
  • Publication Date: 2017
  • Doi Number: 10.1016/j.dam.2016.10.013
  • Journal Name: DISCRETE APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.582-588
  • Hacettepe University Affiliated: Yes

Abstract

We study the maximum number of hyperedges in a 3-uniform hypergraph on n vertices that does not contain a Berge cycle of a given length l. In particular we prove that the upper bound for C2k+1-free hypergraphs is of the order O(k(2)n(1+1/k)), improving the upper bound of Gyori and Lemons (2012) by a factor of Theta (k(2)). Similar bounds are shown for linear hypergraphs. (C) 2016 Elsevier B.V. All rights reserved.