{"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/bridge-indices-of-spatial-graphs-and-diagram","title":"Bridge indices of spatial graphs and diagram colorings","arxiv_id":"2410.23253","date":"2024-10-30","proceeding":null,"authors":["Sarah Blackwell","Puttipong Pongtanapaisan","Hanh Vo"],"abstract":"We extend the Wirtinger number of links, an invariant originally defined by Blair, Kjuchukova, Velazquez, and Villanueva in terms of extending initial colorings of some strands of a diagram to the entire diagram, to spatial graphs. We prove that the Wirtinger number equals the bridge index of spatial graphs, and we implement an algorithm in Python which gives a more efficient way to estimate upper bounds of bridge indices. Combined with lower bounds from diagram colorings by elements from certain algebraic structures and clasping techniques, we obtain exact bridge indices for a large family of almost unknotted spatial graphs. We also show that for every possible negative Euler characteristic, there exist almost unknotted graphs of arbitrarily large bridge index.","url_abs":"https://arxiv.org/abs/2410.23253v1","url_pdf":"https://arxiv.org/pdf/2410.23253v1.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":"bridge-indices-of-spatial-graphs-and-diagram","repo_url":"https://github.com/hanhv/graph-wirt","is_official":1,"mentioned_in_paper":0,"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}