{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T20:21:09Z","timestamp":1772223669918,"version":"3.50.1"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2024,9,20]],"date-time":"2024-09-20T00:00:00Z","timestamp":1726790400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2024,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Given a family of graphs <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000245_inline1.png\"\/><jats:tex-math>\n$\\mathcal{F}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and an integer <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000245_inline2.png\"\/><jats:tex-math>\n$r$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, we say that a graph is <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000245_inline3.png\"\/><jats:tex-math>\n$r$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-Ramsey for <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000245_inline4.png\"\/><jats:tex-math>\n$\\mathcal{F}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> if any <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000245_inline5.png\"\/><jats:tex-math>\n$r$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-colouring of its edges admits a monochromatic copy of a graph from <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000245_inline6.png\"\/><jats:tex-math>\n$\\mathcal{F}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. The threshold for the classic Ramsey property, where <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000245_inline7.png\"\/><jats:tex-math>\n$\\mathcal{F}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> consists of one graph, in the binomial random graph was located in the celebrated work of R\u00f6dl and Ruci\u0144ski.<\/jats:p><jats:p>In this paper, we offer a twofold generalisation to the R\u00f6dl\u2013Ruci\u0144ski theorem. First, we show that the list-colouring version of the property has the same threshold. Second, we extend this result to finite families <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000245_inline8.png\"\/><jats:tex-math>\n$\\mathcal{F}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, where the threshold statements might also diverge. This also confirms further special cases of the Kohayakawa\u2013Kreuter conjecture. Along the way, we supply a short(-ish), self-contained proof of the <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000245_inline9.png\"\/><jats:tex-math>\n$0$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-statement of the R\u00f6dl\u2013Ruci\u0144ski theorem.<\/jats:p>","DOI":"10.1017\/s0963548324000245","type":"journal-article","created":{"date-parts":[[2024,9,20]],"date-time":"2024-09-20T09:23:53Z","timestamp":1726824233000},"page":"829-851","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":2,"title":["The List-Ramsey threshold for families of graphs"],"prefix":"10.1017","volume":"33","author":[{"given":"Eden","family":"Kuperwasser","sequence":"first","affiliation":[]},{"given":"Wojciech","family":"Samotij","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2024,9,20]]},"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548324000245","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,11]],"date-time":"2024-11-11T13:24:59Z","timestamp":1731331499000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548324000245\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,20]]},"references-count":0,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2024,11]]}},"alternative-id":["S0963548324000245"],"URL":"https:\/\/doi.org\/10.1017\/s0963548324000245","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,9,20]]},"assertion":[{"value":"\u00a9 The Author(s), 2024. 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-NonCommercial-NoDerivatives licence (https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is unaltered and is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use or in order to create a derivative work.","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"}]}}