{"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/a-common-variable-minimax-theorem-for-graphs","title":"A common variable minimax theorem for graphs","arxiv_id":"2107.14747","date":"2021-07-30","proceeding":null,"authors":["Ronald R. Coifman","Nicholas F. Marshall","Stefan Steinerberger"],"abstract":"Let $\\mathcal{G} = \\{G_1 = (V, E_1), \\dots, G_m = (V, E_m)\\}$ be a collection of $m$ graphs defined on a common set of vertices $V$ but with different edge sets $E_1, \\dots, E_m$. Informally, a function $f :V \\rightarrow \\mathbb{R}$ is smooth with respect to $G_k = (V,E_k)$ if $f(u) \\sim f(v)$ whenever $(u, v) \\in E_k$. We study the problem of understanding whether there exists a nonconstant function that is smooth with respect to all graphs in $\\mathcal{G}$, simultaneously, and how to find it if it exists.","url_abs":"https://arxiv.org/abs/2107.14747v1","url_pdf":"https://arxiv.org/pdf/2107.14747v1.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":"abstracts"},"code_links":[{"paper_slug":"a-common-variable-minimax-theorem-for-graphs","repo_url":"https://github.com/sarihl/common-variable-multi-graph","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}