# A note on the Tur\'an number of a Berge odd cycle

## TL;DR

This paper improves upper bounds on the number of hyperedges in 3-uniform hypergraphs avoiding Berge odd cycles, extending previous results and providing new insights into Berge cliques.

## Contribution

It presents tighter bounds on hyperedge counts for Berge odd cycles and introduces a more general theorem that enhances prior work.

## Key findings

- Improved upper bounds for Berge odd cycle-free hypergraphs
- New results on Berge cliques
- Extension of previous bounds by F"uredi and "Ozkahya

## Abstract

In this note we obtain upper bounds on the number of hyperedges in 3-uniform hypergraphs not containing a Berge cycle of given odd length. We improve the bound given by F\"uredi and \"Ozkahya in 2017. The result follows from a more general theorem. We also obtain some new results for Berge cliques.