The codegree Turán density of $3$-uniform tight cycles
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916346819772416 |
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| author | Piga, Simón Sanhueza-Matamala, Nicolás Schacht, Mathias |
| author_facet | Piga, Simón Sanhueza-Matamala, Nicolás Schacht, Mathias |
| contents | Given any $\varepsilon>0$ we prove that every sufficiently large $n$-vertex $3$-graph $H$ where every pair of vertices is contained in at least $(1/3+\varepsilon)n$ edges contains a copy of $C_{10}$, i.e.\ the tight cycle on $10$ vertices. In fact we obtain the same conclusion for every cycle $C_\ell$ with $\ell\geq 19$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02588 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The codegree Turán density of $3$-uniform tight cycles Piga, Simón Sanhueza-Matamala, Nicolás Schacht, Mathias Combinatorics 05D99, 05C65 Given any $\varepsilon>0$ we prove that every sufficiently large $n$-vertex $3$-graph $H$ where every pair of vertices is contained in at least $(1/3+\varepsilon)n$ edges contains a copy of $C_{10}$, i.e.\ the tight cycle on $10$ vertices. In fact we obtain the same conclusion for every cycle $C_\ell$ with $\ell\geq 19$. |
| title | The codegree Turán density of $3$-uniform tight cycles |
| topic | Combinatorics 05D99, 05C65 |
| url | https://arxiv.org/abs/2408.02588 |