{"arxiv":1,"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.","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"oa_version":"Published Version","page":"559-564","has_accepted_license":"1","article_type":"original","file":[{"file_name":"2025_CombProbComputing_Christoph.pdf","date_updated":"2025-08-05T12:54:06Z","file_size":188818,"relation":"main_file","creator":"dernst","success":1,"access_level":"open_access","file_id":"20135","checksum":"98491e59b4f0d05d69f608bbd5706f1a","content_type":"application/pdf","date_created":"2025-08-05T12:54:06Z"}],"project":[{"call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","isi":1,"ec_funded":1,"type":"journal_article","file_date_updated":"2025-08-05T12:54:06Z","volume":34,"scopus_import":"1","month":"07","publication_identifier":{"issn":["0963-5483"],"eissn":["1469-2163"]},"OA_type":"hybrid","intvolume":"        34","citation":{"chicago":"Christoph, Micha, Kalina H Petrova, and Raphael Steiner. “A Note on Digraph Splitting.” <i>Combinatorics Probability and Computing</i>. Cambridge University Press, 2025. <a href=\"https://doi.org/10.1017/S0963548325000045\">https://doi.org/10.1017/S0963548325000045</a>.","ieee":"M. Christoph, K. H. Petrova, and R. Steiner, “A note on digraph splitting,” <i>Combinatorics Probability and Computing</i>, vol. 34, no. 4. Cambridge University Press, pp. 559–564, 2025.","apa":"Christoph, M., Petrova, K. H., &#38; Steiner, R. (2025). A note on digraph splitting. <i>Combinatorics Probability and Computing</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/S0963548325000045\">https://doi.org/10.1017/S0963548325000045</a>","mla":"Christoph, Micha, et al. “A Note on Digraph Splitting.” <i>Combinatorics Probability and Computing</i>, vol. 34, no. 4, Cambridge University Press, 2025, pp. 559–64, doi:<a href=\"https://doi.org/10.1017/S0963548325000045\">10.1017/S0963548325000045</a>.","short":"M. Christoph, K.H. Petrova, R. Steiner, Combinatorics Probability and Computing 34 (2025) 559–564.","ista":"Christoph M, Petrova KH, Steiner R. 2025. A note on digraph splitting. Combinatorics Probability and Computing. 34(4), 559–564.","ama":"Christoph M, Petrova KH, Steiner R. A note on digraph splitting. <i>Combinatorics Probability and Computing</i>. 2025;34(4):559-564. doi:<a href=\"https://doi.org/10.1017/S0963548325000045\">10.1017/S0963548325000045</a>"},"date_created":"2025-04-06T22:01:32Z","title":"A note on digraph splitting","publication":"Combinatorics Probability and Computing","date_published":"2025-07-01T00:00:00Z","year":"2025","article_processing_charge":"Yes (in subscription journal)","publisher":"Cambridge University Press","OA_place":"publisher","quality_controlled":"1","oa":1,"external_id":{"isi":["001449245700001"],"arxiv":["2310.08449"]},"day":"01","date_updated":"2025-09-30T11:26:00Z","_id":"19503","department":[{"_id":"MaKw"}],"issue":"4","language":[{"iso":"eng"}],"author":[{"full_name":"Christoph, Micha","last_name":"Christoph","first_name":"Micha"},{"first_name":"Kalina H","last_name":"Petrova","full_name":"Petrova, Kalina H","id":"554ff4e4-f325-11ee-b0c4-a10dbd523381"},{"first_name":"Raphael","last_name":"Steiner","full_name":"Steiner, Raphael"}],"publication_status":"published","abstract":[{"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.","lang":"eng"}],"status":"public","ddc":["510"],"license":"https://creativecommons.org/licenses/by/4.0/","doi":"10.1017/S0963548325000045"}