English

$3$-uniform hypergraphs without a cycle of length five

Combinatorics 2019-02-19 v1

Abstract

In this paper we show that the maximum number of hyperedges in a 33-uniform hypergraph on nn vertices without a (Berge) cycle of length five is less than (0.254+o(1))n3/2(0.254 + o(1))n^{3/2}, improving an estimate of Bollob\'as and Gy\H{o}ri. We obtain this result by showing that not many 33-paths can start from certain subgraphs of the shadow.

Keywords

Cite

@article{arxiv.1902.06257,
  title  = {$3$-uniform hypergraphs without a cycle of length five},
  author = {Beka Ergemlidze and Ervin Győri and Abhishek Methuku},
  journal= {arXiv preprint arXiv:1902.06257},
  year   = {2019}
}
R2 v1 2026-06-23T07:42:59.098Z