### Abstract

Let n≥k≥r+3 and H be an n-vertex r-uniform hypergraph. We show that if |H|>[Formula presented](k−1r) then H contains a Berge cycle of length at least k. This bound is tight when k−2 divides n−1. We also show that the bound is attained only for connected r-uniform hypergraphs in which every block is the complete hypergraph K_{k−1}
^{(r)}.

Original language | English |
---|---|

Journal | Journal of Combinatorial Theory. Series B |

DOIs | |

Publication status | Accepted/In press - Jan 1 2018 |

### Fingerprint

### Keywords

- Berge cycles
- Extremal hypergraph theory

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

### Cite this

*Journal of Combinatorial Theory. Series B*. https://doi.org/10.1016/j.jctb.2018.12.001

**Avoiding long Berge cycles.** / Füredi, Z.; Kostochka, Alexandr; Luo, Ruth.

Research output: Contribution to journal › Article

*Journal of Combinatorial Theory. Series B*. https://doi.org/10.1016/j.jctb.2018.12.001

}

TY - JOUR

T1 - Avoiding long Berge cycles

AU - Füredi, Z.

AU - Kostochka, Alexandr

AU - Luo, Ruth

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Let n≥k≥r+3 and H be an n-vertex r-uniform hypergraph. We show that if |H|>[Formula presented](k−1r) then H contains a Berge cycle of length at least k. This bound is tight when k−2 divides n−1. We also show that the bound is attained only for connected r-uniform hypergraphs in which every block is the complete hypergraph Kk−1 (r).

AB - Let n≥k≥r+3 and H be an n-vertex r-uniform hypergraph. We show that if |H|>[Formula presented](k−1r) then H contains a Berge cycle of length at least k. This bound is tight when k−2 divides n−1. We also show that the bound is attained only for connected r-uniform hypergraphs in which every block is the complete hypergraph Kk−1 (r).

KW - Berge cycles

KW - Extremal hypergraph theory

UR - http://www.scopus.com/inward/record.url?scp=85057994672&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85057994672&partnerID=8YFLogxK

U2 - 10.1016/j.jctb.2018.12.001

DO - 10.1016/j.jctb.2018.12.001

M3 - Article

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

SN - 0095-8956

ER -