{"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/every-planar-graph-with-delta-geqslant-8-is","title":"Every planar graph with $Δ\\geqslant 8$ is totally $(Δ+2)$-choosable","arxiv_id":"1904.12060","date":"2019-04-26","proceeding":null,"authors":["Marthe Bonamy","Théo Pierron","Éric Sopena"],"abstract":"Total coloring is a variant of edge coloring where both vertices and edges are to be colored. A graph is totally $k$-choosable if for any list assignment of $k$ colors to each vertex and each edge, we can extract a proper total coloring. In this setting, a graph of maximum degree $\\Delta$ needs at least $\\Delta+1$ colors. In the planar case, Borodin proved in 1989 that $\\Delta+2$ colors suffice when $\\Delta$ is at least 9. We show that this bound also holds when $\\Delta$ is $8$.","url_abs":"https://arxiv.org/abs/1904.12060v4","url_pdf":"https://arxiv.org/pdf/1904.12060v4.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":"every-planar-graph-with-delta-geqslant-8-is","repo_url":"https://github.com/tpierron/Delta8","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}