{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/the-turan-density-of-the-tight-5-cycle-minus","title":"The Turán density of the tight 5-cycle minus one edge","arxiv_id":"2412.21011","date":"2024-12-30","proceeding":null,"authors":["Levente Bodnár","Jared León","Xizhi Liu","Oleg Pikhurko"],"abstract":"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 Tur\\'an 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 Lidick\\'y--Mattes--Pfender [arXiv:2409.14257].","url_abs":"https://arxiv.org/abs/2412.21011v2","url_pdf":"https://arxiv.org/pdf/2412.21011v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"the-turan-density-of-the-tight-5-cycle-minus","repo_url":"https://github.com/bodnalev/supplementary_files","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}