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

Zoltan Furedi; Alexandr Kostochka; Ruth Luo

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arXiv · 1807.06119

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

Zoltan Furedi·Alexandr Kostochka·Ruth Luo

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Abstract

Let $EG_r(n,k)$ 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 $EG_r(n,k)$ and described the structure of extremal hypergraphs for the case when $k-2$ divides $n-1$ and $k\geq r+3$. In this paper we determine $EG_r(n,k)$ and describe the extremal hypergraphs for all $n$ when $k\geq r+4$.

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BibTeX RIS

Zoltan Furedi, Alexandr Kostochka, Ruth Luo. 2018-07-16. Avoiding long Berge cycles II, exact bounds for all $n$. https://arxiv.org/abs/1807.06119

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