{"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/inverting-the-turan-problem","title":"Inverting the Turán Problem","arxiv_id":"1711.02082","date":"2017-11-06","proceeding":null,"authors":["Joseph Briggs","Christopher Cox"],"abstract":"Classical questions in extremal graph theory concern the asymptotics of $\\operatorname{ex}(G, \\mathcal{H})$ where $\\mathcal{H}$ is a fixed family of graphs and $G=G_n$ is taken from a `standard' increasing sequence of host graphs $(G_1, G_2, \\dots)$, most often $K_n$ or $K_{n,n}$. Inverting the question, we can instead ask how large $e(G)$ can be with respect to $\\operatorname{ex}(G,\\mathcal{H})$. We show that the standard sequences indeed maximize $e(G)$ for some choices of $\\mathcal{H}$, but not for others. Many interesting questions and previous results arise very naturally in this context, which also, unusually, gives rise to sensible extremal questions concerning multigraphs and non-uniform hypergraphs.","url_abs":"http://arxiv.org/abs/1711.02082v2","url_pdf":"http://arxiv.org/pdf/1711.02082v2.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":"inverting-the-turan-problem","repo_url":"https://github.com/cocox-math/inverse-turan","is_official":1,"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}