{"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/on-contractible-transformations-of-graphs","title":"Collapsibility and homological properties of $\\mathfrak{I}$-contractible transformations","arxiv_id":"1808.07461","date":"2018-08-22","proceeding":null,"authors":["Jesus F. Espinoza","Martín-Eduardo Frías-Armenta","Héctor A. Hernández"],"abstract":"The family of $\\mathfrak{I}$-contractible graphs and contractible transformations was defined by A. Ivashchenko in the mid-90's. In this paper we study the collapsibility and homological properties of the clique complex associated to $\\mathfrak{I}$-contractible graphs. We show that for any graph in a special subfamily of the $\\mathfrak{I}$-contractible graphs (the strong $\\mathfrak{I}$-contractible ones) its clique complex is collapsible. Moreover, we present an algorithm that allows us to verify if any graph is strong $\\mathfrak{I}$-contractible, as well as an algorithm to delete those vertices whose open neighborhood is also strong $\\mathfrak{I}$-contractible. Finally, we show how to use these algorithms to compute the persistent homology of an arbitrary Vietoris-Rips complex for applications in topological data analysis.","url_abs":"https://arxiv.org/abs/1808.07461v5","url_pdf":"https://arxiv.org/pdf/1808.07461v5.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":"on-contractible-transformations-of-graphs","repo_url":"https://github.com/Geometric-and-Combinatorial-Structures/contractible-graphs","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}