On \(3\)-uniform hypergraphs avoiding a cycle of length four

DOI10.37236/11443arXiv2008.11372OpenAlexW3080247078MaRDI QIDQ6197309

Abhishek Methuku, Ervin Gyoeri, Beka Ergemlidze, Nika Salia, Casey Tompkins

Publication date: 16 February 2024

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

Abstract: In this note we show that the maximum number of edges in a $3$-uniform hypergraph without a Berge cycle of length four is at most $(1+o(1))frac{n}^{3/2}sqrt10$. This improves earlier estimates by GyH{o}ri and Lemons and by F"uredi and "Ozkahya.

Full work available at URL: https://arxiv.org/abs/2008.11372

zbMATH Keywords

cyclesextremal graphstriple systemsTurán number

Mathematics Subject Classification ID

Hypergraphs (05C65) Enumeration in graph theory (05C30) Paths and cycles (05C38) Distance in graphs (05C12)

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