{"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/partitioning-edges-of-a-planar-graph-into","title":"Partitioning edges of a planar graph into linear forests and a matching","arxiv_id":"2302.13312","date":"2023-02-26","proceeding":null,"authors":["Marthe Bonamy","Jadwiga Czyżewska","Łukasz Kowalik","Michał Pilipczuk"],"abstract":"We show that the edges of any planar graph of maximum degree at most $9$ can be partitioned into $4$ linear forests and a matching. Combined with known results, this implies that the edges of any planar graph $G$ of odd maximum degree $\\Delta\\ge 9$ can be partitioned into $\\tfrac{\\Delta-1}{2}$ linear forests and one matching. This strengthens well-known results stating that graphs in this class have chromatic index $\\Delta$ [Vizing, 1965] and linear arboricity at most $\\lceil(\\Delta+1)/2\\rceil$ [Wu, 1999].","url_abs":"https://arxiv.org/abs/2302.13312v1","url_pdf":"https://arxiv.org/pdf/2302.13312v1.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":"partitioning-edges-of-a-planar-graph-into","repo_url":"https://github.com/lkowalik/linear-arboricity","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","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}