Avoiding long Berge cycles, the missing cases $k=r+1$ and $k=r+2$

Abstract

The maximum size of an $r$-uniform hypergraph without a Berge cycle of length at least $k$ has been determined for all $k\ge r+3$ by Füredi, Kostochka and Luo and for $k<r$ (and $k=r$, asymptotically) by Kostochka and Luo. In this paper, we settle the remaining cases: $k=r+1$ and $k=r+2$, proving a conjecture of Füredi, Kostochka and Luo.

References in corpus (3)

• On $r$-uniform hypergraphs with circumference less than $r$
• Avoiding long Berge cycles II, exact bounds for all $n$
• Avoiding long Berge cycles

Cited by in corpus (4)

• The extremal $p$-spectral radius of Berge-hypergraphs
• Berge cycles in non-uniform hypergraphs
• On 2-connected hypergraphs with no long cycles
• On the cover Ramsey number of Berge hypergraphs