# The Structure of Hypergraphs without long Berge cycles

## TL;DR

This paper investigates the structure of r-uniform hypergraphs without long Berge cycles, identifying their special substructure and determining their extremal number, thus resolving conjectures and recent results in the field.

## Contribution

It characterizes the structure of hypergraphs without long Berge cycles and determines their extremal number, confirming conjectures and simplifying recent findings.

## Key findings

- Determined the extremal number for hypergraphs without long Berge cycles.
- Identified the special substructure of such hypergraphs.
- Confirmed the conjectured value for the extremal number when k=r.

## Abstract

We study the structure of $r$-uniform hypergraphs containing no Berge cycles of length at least $k$ for $k \leq r$, and determine that such hypergraphs have some special substructure. In particular we determine the extremal number of such hypergraphs, giving an affirmative answer to the conjectured value when $k=r$ and giving a a simple solution to a recent result of Kostochka-Luo when $k < r$.