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

Zoltan Furedi; Alexandr Kostochka; Ruth Luo

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

Combinatorics 2018-07-18 v1

Authors: Zoltan Furedi , Alexandr Kostochka , Ruth Luo

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 $k\geq r+4$ .

Keywords

hypergraph theory graph cycles turán theory

Cite

@article{arxiv.1807.06119,
  title  = {Avoiding long Berge cycles II, exact bounds for all $n$},
  author = {Zoltan Furedi and Alexandr Kostochka and Ruth Luo},
  journal= {arXiv preprint arXiv:1807.06119},
  year   = {2018}
}

Comments

arXiv admin note: text overlap with arXiv:1805.04195

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

Abstract

Keywords

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