{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T21:58:54Z","timestamp":1747173534597,"version":"3.40.5"},"reference-count":28,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2023,11,8]],"date-time":"2023-11-08T00:00:00Z","timestamp":1699401600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2024,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In 2003, Bohman, Frieze, and Martin initiated the study of randomly perturbed graphs and digraphs. For digraphs, they showed that for every <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000391_inline1.png\"\/><jats:tex-math>\n$\\alpha \\gt 0$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, there exists a constant <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000391_inline2.png\"\/><jats:tex-math>\n$C$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> such that for every <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000391_inline3.png\"\/><jats:tex-math>\n$n$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-vertex digraph of minimum semi-degree at least <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000391_inline4.png\"\/><jats:tex-math>\n$\\alpha n$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, if one adds <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000391_inline5.png\"\/><jats:tex-math>\n$Cn$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> random edges then asymptotically almost surely the resulting digraph contains a consistently oriented Hamilton cycle. We generalize their result, showing that the hypothesis of this theorem actually asymptotically almost surely ensures the existence of every orientation of a cycle of every possible length, simultaneously. Moreover, we prove that we can relax the minimum semi-degree condition to a minimum total degree condition when considering orientations of a cycle that do not contain a large number of vertices of indegree <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000391_inline6.png\"\/><jats:tex-math>\n$1$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. Our proofs make use of a variant of an absorbing method of Montgomery.<\/jats:p>","DOI":"10.1017\/s0963548323000391","type":"journal-article","created":{"date-parts":[[2023,11,8]],"date-time":"2023-11-08T01:10:45Z","timestamp":1699405845000},"page":"157-178","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":2,"title":["On oriented cycles in randomly perturbed digraphs"],"prefix":"10.1017","volume":"33","author":[{"given":"Igor","family":"Araujo","sequence":"first","affiliation":[]},{"given":"J\u00f3zsef","family":"Balogh","sequence":"additional","affiliation":[]},{"given":"Robert A.","family":"Krueger","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4451-7821","authenticated-orcid":false,"given":"Sim\u00f3n","family":"Piga","sequence":"additional","affiliation":[]},{"given":"Andrew","family":"Treglown","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2023,11,8]]},"reference":[{"doi-asserted-by":"publisher","key":"S0963548323000391_ref10","DOI":"10.1090\/tran\/7727"},{"doi-asserted-by":"publisher","key":"S0963548323000391_ref6","DOI":"10.1002\/rsa.20850"},{"doi-asserted-by":"publisher","key":"S0963548323000391_ref16","DOI":"10.37236\/9510"},{"doi-asserted-by":"publisher","key":"S0963548323000391_ref4","DOI":"10.1016\/0095-8956(71)90016-5"},{"key":"S0963548323000391_ref13","first-page":"495","article-title":"Une condition suffisante d\u2019existence d\u2019un circuit hamiltonien","volume":"25","author":"Ghouila-Houri","year":"1960","journal-title":"C. R. Acad. Sci. Paris"},{"key":"S0963548323000391_ref5","first-page":"181","volume-title":"Colloq. Math. Soc. J\u00e1nos Bolyai, Keszthely","author":"Bondy","year":"1973"},{"doi-asserted-by":"publisher","key":"S0963548323000391_ref9","DOI":"10.1112\/plms\/s3-2.1.69"},{"doi-asserted-by":"publisher","key":"S0963548323000391_ref20","DOI":"10.1017\/S0963548316000079"},{"doi-asserted-by":"publisher","key":"S0963548323000391_ref3","DOI":"10.1002\/rsa.10070"},{"doi-asserted-by":"publisher","key":"S0963548323000391_ref7","DOI":"10.1137\/140974675"},{"key":"S0963548323000391_ref14","first-page":"205","article-title":"Antidirected Hamilton cycles in digraphs","volume":"10","author":"Grant","year":"1980","journal-title":"Ars Combin."},{"doi-asserted-by":"publisher","key":"S0963548323000391_ref18","DOI":"10.1002\/rsa.20886"},{"doi-asserted-by":"publisher","key":"S0963548323000391_ref22","DOI":"10.2307\/1426987"},{"doi-asserted-by":"publisher","key":"S0963548323000391_ref15","DOI":"10.1002\/jgt.3190190404"},{"doi-asserted-by":"publisher","key":"S0963548323000391_ref11","DOI":"10.1017\/fms.2020.29"},{"doi-asserted-by":"publisher","key":"S0963548323000391_ref8","DOI":"10.37236\/3610"},{"doi-asserted-by":"publisher","key":"S0963548323000391_ref23","DOI":"10.1016\/j.aim.2019.106793"},{"unstructured":"[24] Montgomery, R. (2014) Embedding bounded degree spanning trees in random graphs, arXiv: 1405.6559.","key":"S0963548323000391_ref24"},{"unstructured":"[26] Morawski, P. and Petrova, K. (2023) Randomly perturbed digraphs also have bounded-degree spanning trees, arXiv: 2306.14648.","key":"S0963548323000391_ref26"},{"doi-asserted-by":"publisher","key":"S0963548323000391_ref27","DOI":"10.1016\/j.ejc.2020.103118"},{"doi-asserted-by":"publisher","key":"S0963548323000391_ref1","DOI":"10.5817\/CZ.MUNI.EUROCOMB23-009"},{"doi-asserted-by":"publisher","key":"S0963548323000391_ref12","DOI":"10.1002\/rsa.20796"},{"unstructured":"[25] Montgomery, R. (2021) Spanning cycles in random directed graphs, arXiv: 2103.06751.","key":"S0963548323000391_ref25"},{"doi-asserted-by":"publisher","key":"S0963548323000391_ref17","DOI":"10.1002\/rsa.20981"},{"doi-asserted-by":"publisher","key":"S0963548323000391_ref21","DOI":"10.1137\/15M1032910"},{"doi-asserted-by":"crossref","unstructured":"[19] Krivelevich, M. (1997) Triangle factors in random graphs. Combin. Probab. Comput. 6 337\u2013347.","key":"S0963548323000391_ref19","DOI":"10.1017\/S0963548397003106"},{"doi-asserted-by":"publisher","key":"S0963548323000391_ref28","DOI":"10.1017\/S0963548305007042"},{"doi-asserted-by":"publisher","key":"S0963548323000391_ref2","DOI":"10.1016\/j.jctb.2011.10.002"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548323000391","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,5]],"date-time":"2024-02-05T11:22:58Z","timestamp":1707132178000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548323000391\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,8]]},"references-count":28,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,3]]}},"alternative-id":["S0963548323000391"],"URL":"https:\/\/doi.org\/10.1017\/s0963548323000391","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"type":"print","value":"0963-5483"},{"type":"electronic","value":"1469-2163"}],"subject":[],"published":{"date-parts":[[2023,11,8]]},"assertion":[{"value":"\u00a9 The Author(s), 2023. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}