{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","has_accepted_license":"1","publication":"Combinatorics Probability and Computing","title":"A note on digraph splitting","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png"},"publisher":"Cambridge University Press","doi":"10.1017/S0963548325000045","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1469-2163"],"issn":["0963-5483"]},"OA_type":"hybrid","ec_funded":1,"article_type":"original","arxiv":1,"status":"public","external_id":{"arxiv":["2310.08449"]},"author":[{"full_name":"Christoph, Micha","last_name":"Christoph","first_name":"Micha"},{"full_name":"Petrova, Kalina H","id":"554ff4e4-f325-11ee-b0c4-a10dbd523381","first_name":"Kalina H","last_name":"Petrova"},{"first_name":"Raphael","last_name":"Steiner","full_name":"Steiner, Raphael"}],"oa_version":"Published Version","scopus_import":"1","date_published":"2025-03-21T00:00:00Z","OA_place":"publisher","_id":"19503","month":"03","article_processing_charge":"No","department":[{"_id":"MaKw"}],"date_created":"2025-04-06T22:01:32Z","project":[{"call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413"}],"date_updated":"2025-04-14T07:54:58Z","publication_status":"epub_ahead","type":"journal_article","abstract":[{"lang":"eng","text":"A tantalizing open problem, posed independently by Stiebitz in 1995 and by Alon in 1996 and again in 2006, asks whether for every pair of integers  s,t≥1 there exists a finite number  F(s,t)\r\nsuch that the vertex set of every digraph of minimum out-degree at least  F(s,t) can be partitioned into non-empty parts  A  and  B  such that the subdigraphs induced on  A\r\n  and  B  have minimum out-degree at least  s  and  t , respectively.\r\nIn this short note, we prove that if  F(2,2)  exists, then all the numbers  F(s,t)  with  s,t≥1\r\n  exist and satisfy  F(s,t)=Θ(s+t) . In consequence, the problem of Alon and Stiebitz reduces to the case  s=t=2 . Moreover, the numbers  F(s,t)  with  s,t≥2  either all exist and grow linearly, or all of them do not exist."}],"acknowledgement":"Funded by SNSF Ambizione grant No. 216071. 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. Funded by SNSF grant CRSII5, 173721.","day":"21","year":"2025"}