Salia, Nika

The structure of hypergraphs without long Berge cycles

Here, we study the structure of r-uniform hypergraphs containing no Berge cycles of length at least k for k ≤ 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 simple solution to a recent result of Kostochka-Luo when k < r.