{"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/exact-generalized-turan-number-for-k-3-versus","title":"Exact generalized Turán number for $K_3$ versus suspension of $P_4$","arxiv_id":"2307.04369","date":"2023-07-10","proceeding":null,"authors":["Sayan Mukherjee"],"abstract":"Let $P_4$ denote the path graph on $4$ vertices. The suspension of $P_4$, denoted by $\\widehat P_4$, is the graph obtained via adding an extra vertex and joining it to all four vertices of $P_4$. In this note, we demonstrate that for $n\\ge 8$, the maximum number of triangles in any $n$-vertex graph not containing $\\widehat P_4$ is $\\left\\lfloor n^2/8\\right\\rfloor$. Our method uses simple induction along with computer programming to prove a base case of the induction hypothesis.","url_abs":"https://arxiv.org/abs/2307.04369v1","url_pdf":"https://arxiv.org/pdf/2307.04369v1.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":"exact-generalized-turan-number-for-k-3-versus","repo_url":"https://github.com/potla1995/hatp4free","is_official":1,"mentioned_in_paper":1,"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}