On \(3\)-uniform hypergraphs avoiding a cycle of length four (Q6197309)
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scientific article; zbMATH DE number 7806232
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On \(3\)-uniform hypergraphs avoiding a cycle of length four |
scientific article; zbMATH DE number 7806232 |
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On \(3\)-uniform hypergraphs avoiding a cycle of length four (English)
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16 February 2024
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Summary: We show that the maximum number of edges in a \(3\)-uniform hypergraph without a Berge cycle of length four is at most \((1+o(1))\frac{n^{3/2}}{\sqrt{10}}\). This improves earlier estimates by \textit{E. Győri} and \textit{N. Lemons} [Comb. Probab. Comput. 21, No. 1--2, 193--201 (2012; Zbl 1241.05101)] and by \textit{Z. Füredi} and \textit{L. Özkahya} [Discrete Appl. Math. 216, Part 3, 582--588 (2017; Zbl 1358.05203)].
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Turán number
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cycles
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extremal graphs
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triple systems
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