Avoiding long Berge cycles II, exact bounds for all $n$

Abstract

Let $E{G}_r(n,k)$ denote the maximum number of edges in an $n$-vertex $r$-uniform hypergraph with no Berge cycles of length $k$ or longer. In the first part of this work, we have found exact values of $E{G}_r(n,k)$ and described the structure of extremal hypergraphs for the case when $k-2$ divides $n-1$ and $k\ge r+3$. In this paper we determine $E{G}_r(n,k)$ and describe the extremal hypergraphs for all $n$ when $k\ge r+4$.

arXiv admin note: text overlap with arXiv:1805.04195