避免长Berge周期:缺少k = r + 1和k = r + 2的情况

Combinatorics, Probability and Computing Pub Date : 2018-08-23 DOI:10.1017/S0963548319000415

Beka Ergemlidze, E. Györi, Abhishek Methuku, Nika Salia, C. Tompkins, Oscar Zamora

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引用次数: 17

摘要

摘要本文用f redi、Kostochka和Luo分别求出了对于所有k≥r + 3，以及对于k < r(且k = r，渐近地)，无Berge环的r-一致超图的最大尺寸。本文解决了k = r + 1和k = r + 2的剩余情况，证明了f redi, Kostochka和Luo的一个猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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.

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Combinatorics, Probability and Computing

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