The Turán density of the tight 5-cycle minus one edge
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866918086655868928 |
|---|---|
| author | Bodnár, Levente León, Jared Liu, Xizhi Pikhurko, Oleg |
| author_facet | Bodnár, Levente León, Jared Liu, Xizhi Pikhurko, Oleg |
| contents | Let the tight $\ell$-cycle minus one edge $C_\ell^{3-}$ be the $3$-graph on $\{1,\dots,\ell\}$ consisting of $\ell-1$ consecutive triples in the cyclic order. We show that, for every $\ell\ge 5$ not divisible by $3$, the Turán density of $C_{\ell}^{3-}$ is $1/4$ and also prove some finer structure results. This proves a conjecture of Mubayi--Sudakov--Pikhurko from 2011 and extends the results of Balogh--Luo [Combinatorica 44 (2024) 949--976] who established analogous claims for all sufficiently large $\ell$.
Results similar to ours were independently obtained by Lidický--Mattes--Pfender [arXiv:2409.14257]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_21011 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Turán density of the tight 5-cycle minus one edge Bodnár, Levente León, Jared Liu, Xizhi Pikhurko, Oleg Combinatorics 05C35, 05C65 Let the tight $\ell$-cycle minus one edge $C_\ell^{3-}$ be the $3$-graph on $\{1,\dots,\ell\}$ consisting of $\ell-1$ consecutive triples in the cyclic order. We show that, for every $\ell\ge 5$ not divisible by $3$, the Turán density of $C_{\ell}^{3-}$ is $1/4$ and also prove some finer structure results. This proves a conjecture of Mubayi--Sudakov--Pikhurko from 2011 and extends the results of Balogh--Luo [Combinatorica 44 (2024) 949--976] who established analogous claims for all sufficiently large $\ell$. Results similar to ours were independently obtained by Lidický--Mattes--Pfender [arXiv:2409.14257]. |
| title | The Turán density of the tight 5-cycle minus one edge |
| topic | Combinatorics 05C35, 05C65 |
| url | https://arxiv.org/abs/2412.21011 |