Infinitely many accumulation points of codegree Turán densities
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911416850579456 |
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| author | Li, Heng Liu, Weichan Schülke, Bjarne Sun, Wanting |
| author_facet | Li, Heng Liu, Weichan Schülke, Bjarne Sun, Wanting |
| contents | The codegree Turán density $γ(F)$ of a $k$-graph $F$ is the smallest $γ\in[0,1)$ such that every $k$-graph $H$ with $δ_{k-1}(H)\geq(γ+o(1))\vert V(H)\vert$ contains a copy of $F$. We prove that for all $k,r\in\mathbb{N}$ with $k\geq3$, $\frac{r-1}{r}$ is an accumulation point of $Γ^{(k)}=\{γ(F):F\text{ is a }k\text{-graph}\}$. This makes progress on a problem posed by Mubayi and Zhao. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_13485 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infinitely many accumulation points of codegree Turán densities Li, Heng Liu, Weichan Schülke, Bjarne Sun, Wanting Combinatorics 05C65, 05C35, 05C42 The codegree Turán density $γ(F)$ of a $k$-graph $F$ is the smallest $γ\in[0,1)$ such that every $k$-graph $H$ with $δ_{k-1}(H)\geq(γ+o(1))\vert V(H)\vert$ contains a copy of $F$. We prove that for all $k,r\in\mathbb{N}$ with $k\geq3$, $\frac{r-1}{r}$ is an accumulation point of $Γ^{(k)}=\{γ(F):F\text{ is a }k\text{-graph}\}$. This makes progress on a problem posed by Mubayi and Zhao. |
| title | Infinitely many accumulation points of codegree Turán densities |
| topic | Combinatorics 05C65, 05C35, 05C42 |
| url | https://arxiv.org/abs/2502.13485 |