{"publication_status":"submitted","date_updated":"2026-02-10T11:39:16Z","department":[{"_id":"MaKw"}],"date_created":"2026-02-10T11:32:41Z","article_processing_charge":"No","type":"preprint","doi":"10.48550/arXiv.2508.00480","publication":"arXiv","day":"01","author":[{"full_name":"Montgomery, Richard","first_name":"Richard","last_name":"Montgomery"},{"id":"554ff4e4-f325-11ee-b0c4-a10dbd523381","last_name":"Petrova","first_name":"Kalina H","full_name":"Petrova, Kalina H"},{"full_name":"Ranganathan, Arjun","last_name":"Ranganathan","first_name":"Arjun"},{"last_name":"Tan","first_name":"Jane","full_name":"Tan, Jane"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","year":"2025","ec_funded":1,"external_id":{"arxiv":["2508.00480"]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2508.00480"}],"project":[{"name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"citation":{"ama":"Montgomery R, Petrova KH, Ranganathan A, Tan J. Packing subdivisions into regular graphs. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2508.00480\">10.48550/arXiv.2508.00480</a>","chicago":"Montgomery, Richard, Kalina H Petrova, Arjun Ranganathan, and Jane Tan. “Packing Subdivisions into Regular Graphs.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2508.00480\">https://doi.org/10.48550/arXiv.2508.00480</a>.","short":"R. Montgomery, K.H. Petrova, A. Ranganathan, J. Tan, ArXiv (n.d.).","mla":"Montgomery, Richard, et al. “Packing Subdivisions into Regular Graphs.” <i>ArXiv</i>, 2508.00480, doi:<a href=\"https://doi.org/10.48550/arXiv.2508.00480\">10.48550/arXiv.2508.00480</a>.","apa":"Montgomery, R., Petrova, K. H., Ranganathan, A., &#38; Tan, J. (n.d.). Packing subdivisions into regular graphs. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2508.00480\">https://doi.org/10.48550/arXiv.2508.00480</a>","ista":"Montgomery R, Petrova KH, Ranganathan A, Tan J. Packing subdivisions into regular graphs. arXiv, 2508.00480.","ieee":"R. Montgomery, K. H. Petrova, A. Ranganathan, and J. Tan, “Packing subdivisions into regular graphs,” <i>arXiv</i>. ."},"article_number":"2508.00480","_id":"21211","arxiv":1,"oa":1,"title":"Packing subdivisions into regular graphs","month":"08","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"We show that, for any graph F and η > 0, there exists a d0 = d0(F, η) such that every nvertex d-regular graph with d ≥ d0 has a collection of vertex-disjoint F-subdivisions covering\r\nat least (1 − η)n vertices. This verifies a conjecture of Verstraëte from 2002 and improves a\r\nrecent result of Letzter, Methuku and Sudakov which additionally required d to be at least\r\npolylogarithmic in n.\r\n"}],"OA_type":"green","OA_place":"repository","status":"public","date_published":"2025-08-01T00:00:00Z","acknowledgement":"Supported by the European Research Council (ERC) under the European Union Horizon 2020 research and innovation programme (grant agreement No. 947978). This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413."}