{"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/discrete-and-metric-divisorial-gonality-can","title":"Discrete and metric divisorial gonality can be different","arxiv_id":"2106.12568","date":"2021-06-23","proceeding":null,"authors":["Josse van Dobben de Bruyn","Harry Smit","Marieke van der Wegen"],"abstract":"This paper compares the divisorial gonality of a finite graph $G$ to the divisorial gonality of the associated metric graph $\\Gamma(G,\\mathbb{1})$ with unit lengths. We show that $\\text{dgon}(\\Gamma(G,\\mathbb{1}))$ is equal to the minimal divisorial gonality of all regular subdivisions of $G$, and we provide a class of graphs for which this number is strictly smaller than the divisorial gonality of $G$. This settles a conjecture of M. Baker in the negative.","url_abs":"https://arxiv.org/abs/2106.12568v2","url_pdf":"https://arxiv.org/pdf/2106.12568v2.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":"discrete-and-metric-divisorial-gonality-can","repo_url":"https://github.com/gonality/discrete-vs-metric-dgon","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}