The structure of hypergraphs without long Berge cycles

Ervin Győri; Nathan Lemons; Nika Salia; Oscar Zamora

doi:10.1016/j.jctb.2020.04.007

The structure of hypergraphs without long Berge cycles

Ervin Győri
, Nathan Lemons
, Nika Salia
, Oscar Zamora

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We study the structure of r-uniform hypergraphs containing no Berge cycles of length at least k for k≤r, and determine that such hypergraphs have some special substructure. In particular we determine the extremal number of such hypergraphs, giving an affirmative answer to the conjectured value when k=r and giving a simple solution to a recent result of Kostochka-Luo when k<r.

Original language	English
Pages (from-to)	239-250
Number of pages	12
Journal	Journal of Combinatorial Theory. Series B
Volume	148
DOIs	https://doi.org/10.1016/j.jctb.2020.04.007
State	Published - May 2021
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2020 Elsevier Inc.

Keywords

Berge cycles
Berge paths
Extremal hypergraphs

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/j.jctb.2020.04.007

Cite this

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title = "The structure of hypergraphs without long Berge cycles",

abstract = "We study the structure of r-uniform hypergraphs containing no Berge cycles of length at least k for k≤r, and determine that such hypergraphs have some special substructure. In particular we determine the extremal number of such hypergraphs, giving an affirmative answer to the conjectured value when k=r and giving a simple solution to a recent result of Kostochka-Luo when k",

keywords = "Berge cycles, Berge paths, Extremal hypergraphs",

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doi = "10.1016/j.jctb.2020.04.007",

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AU - Győri, Ervin

AU - Lemons, Nathan

AU - Salia, Nika

AU - Zamora, Oscar

PY - 2021/5

Y1 - 2021/5

N2 - We study the structure of r-uniform hypergraphs containing no Berge cycles of length at least k for k≤r, and determine that such hypergraphs have some special substructure. In particular we determine the extremal number of such hypergraphs, giving an affirmative answer to the conjectured value when k=r and giving a simple solution to a recent result of Kostochka-Luo when k

AB - We study the structure of r-uniform hypergraphs containing no Berge cycles of length at least k for k≤r, and determine that such hypergraphs have some special substructure. In particular we determine the extremal number of such hypergraphs, giving an affirmative answer to the conjectured value when k=r and giving a simple solution to a recent result of Kostochka-Luo when k

KW - Berge cycles

KW - Berge paths

KW - Extremal hypergraphs

UR - https://www.scopus.com/pages/publications/85084232392

U2 - 10.1016/j.jctb.2020.04.007

DO - 10.1016/j.jctb.2020.04.007

M3 - Article

AN - SCOPUS:85084232392

SN - 0095-8956

VL - 148

SP - 239

EP - 250

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

ER -

The structure of hypergraphs without long Berge cycles

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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Cite this