3-Uniform Hypergraphs without a Cycle of Length Five

  • Beka Ergemlidze
  • Ervin Győri
  • Abhishek Methuku
DOI: https://doi.org/10.37236/8806

Abstract

In this paper we show that the maximum number of hyperedges in a $3$-uniform hypergraph on $n$ vertices without a (Berge) cycle of length five is less than $(0.254 + o(1))n^{3/2}$, improving an estimate of Bollobás and Győri.

We obtain this result by showing that not many $3$-paths can start from certain subgraphs of the shadow.

Published
2020-05-01
Issue
Volume 27, Issue 2 (2020)
Article Number
P2.16