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

Part of: Graph theory Extremal combinatorics

Published online by Cambridge University Press:  27 November 2019

Beka Ergemlidze ,
Ervin Győri ,
Abhishek Methuku ,
Nika Salia ,
Casey Tompkins  and
Oscar Zamora
Beka Ergemlidze
Affiliation:
Department of Mathematics and its Applications, Central European University, 1051 Budapest, Hungary
Ervin Győri*
Affiliation:
Department of Mathematics and its Applications, Central European University, 1051 Budapest, Hungary Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, 1053 Budapest, Hungary
Abhishek Methuku
Affiliation:
Department of Mathematics and its Applications, Central European University, 1051 Budapest, Hungary École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
Nika Salia
Affiliation:
Department of Mathematics and its Applications, Central European University, 1051 Budapest, Hungary
Casey Tompkins
Affiliation:
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, 1053 Budapest, Hungary
Oscar Zamora
Affiliation:
Department of Mathematics and its Applications, Central European University, 1051 Budapest, Hungary Escuela de Matemática, Universidad de Costa Rica, San José, Costa Rica
*
*Corresponding author. Email: gyori.ervin@renyi.mta.hu
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Abstract

The maximum size of an r-uniform hypergraph without a Berge cycle of length at least k has been determined for all k ≥ 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.

MSC classification

Primary: 05C65: Hypergraphs
Secondary: 05D99: None of the above, but in this section
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 29 , Issue 3 , May 2020 , pp. 423 - 435
Copyright
© Cambridge University Press 2019

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References

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