The Structure of Hypergraphs without long Berge cycles

Abstract

We study the structure of $r$-uniform hypergraphs containing no Berge cycles of length at least $k$ for $k\le r$, 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 $k<r$.

9 pages, 2 figures