{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,7]],"date-time":"2026-06-07T06:32:19Z","timestamp":1780813939080,"version":"3.54.1"},"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":3,"title":["On oriented cycles in randomly perturbed digraphs"],"prefix":"10.1017","volume":"33","author":[{"given":"Igor","family":"Araujo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J\u00f3zsef","family":"Balogh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robert A.","family":"Krueger","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4451-7821","authenticated-orcid":false,"given":"Sim\u00f3n","family":"Piga","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andrew","family":"Treglown","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2023,11,8]]},"reference":[{"key":"S0963548323000391_ref10","doi-asserted-by":"publisher","DOI":"10.1090\/tran\/7727"},{"key":"S0963548323000391_ref6","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20850"},{"key":"S0963548323000391_ref16","doi-asserted-by":"publisher","DOI":"10.37236\/9510"},{"key":"S0963548323000391_ref4","doi-asserted-by":"publisher","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"},{"key":"S0963548323000391_ref9","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-2.1.69"},{"key":"S0963548323000391_ref20","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548316000079"},{"key":"S0963548323000391_ref3","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.10070"},{"key":"S0963548323000391_ref7","doi-asserted-by":"publisher","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."},{"key":"S0963548323000391_ref18","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20886"},{"key":"S0963548323000391_ref22","doi-asserted-by":"publisher","DOI":"10.2307\/1426987"},{"key":"S0963548323000391_ref15","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190190404"},{"key":"S0963548323000391_ref11","doi-asserted-by":"publisher","DOI":"10.1017\/fms.2020.29"},{"key":"S0963548323000391_ref8","doi-asserted-by":"publisher","DOI":"10.37236\/3610"},{"key":"S0963548323000391_ref23","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2019.106793"},{"key":"S0963548323000391_ref24","unstructured":"[24] Montgomery, R. (2014) Embedding bounded degree spanning trees in random graphs, arXiv: 1405.6559."},{"key":"S0963548323000391_ref26","unstructured":"[26] Morawski, P. and Petrova, K. (2023) Randomly perturbed digraphs also have bounded-degree spanning trees, arXiv: 2306.14648."},{"key":"S0963548323000391_ref27","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2020.103118"},{"key":"S0963548323000391_ref1","doi-asserted-by":"publisher","DOI":"10.5817\/CZ.MUNI.EUROCOMB23-009"},{"key":"S0963548323000391_ref12","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20796"},{"key":"S0963548323000391_ref25","unstructured":"[25] Montgomery, R. (2021) Spanning cycles in random directed graphs, arXiv: 2103.06751."},{"key":"S0963548323000391_ref17","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20981"},{"key":"S0963548323000391_ref21","doi-asserted-by":"publisher","DOI":"10.1137\/15M1032910"},{"key":"S0963548323000391_ref19","doi-asserted-by":"crossref","unstructured":"[19] Krivelevich, M. (1997) Triangle factors in random graphs. Combin. Probab. 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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"}]}}