3-uniform hypergraphs without a cycle of length five

DOI10.37236/8806zbMath1444.05100arXiv1902.06257OpenAlexW3021566167MaRDI QIDQ2182003

Abhishek Methuku, Beka Ergemlidze, Ervin Gyoeri

Publication date: 20 May 2020

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Abstract: In this paper we show that the maximum number of hyperedges in a $3$-uniform hypergraph on $n$ vertices without a (Berge) cycle of length five is less than $(0.254 + o(1))n^{3/2}$, improving an estimate of Bollob'as and GyH{o}ri. We obtain this result by showing that not many $3$-paths can start from certain subgraphs of the shadow.

Full work available at URL: https://arxiv.org/abs/1902.06257

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zbMATH Keywords

Berge cyclemaximum number of hyperedges

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Hypergraphs (05C65) Enumeration in graph theory (05C30) Paths and cycles (05C38)

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Related Items (3)

A note on the Tur\'an number of a Berge odd cycle ⋮ On \(3\)-uniform hypergraphs avoiding a cycle of length four ⋮ On 3-uniform hypergraphs without linear cycles

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