{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,18]],"date-time":"2026-02-18T09:28:19Z","timestamp":1771406899280,"version":"3.50.1"},"reference-count":38,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T00:00:00Z","timestamp":1762819200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2026,3]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    A meta-conjecture of Coulson, Keevash, Perarnau, and Yepremyan [12] states that above the extremal threshold for a given spanning structure in a (hyper-)graph, one can find a rainbow version of that spanning structure in any suitably bounded colouring of the host (hyper-)graph. We solve one of the most pertinent outstanding cases of this conjecture by showing that for any\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548325100266_inline1.png\"\/>\n                        <jats:tex-math>$1\\leq j\\leq k-1$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    , if\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548325100266_inline2.png\"\/>\n                        <jats:tex-math>$G$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    is a\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548325100266_inline3.png\"\/>\n                        <jats:tex-math>$k$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    -uniform hypergraph above the\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548325100266_inline4.png\"\/>\n                        <jats:tex-math>$j$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    -degree threshold for a loose Hamilton cycle, then any globally bounded colouring of\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548325100266_inline5.png\"\/>\n                        <jats:tex-math>$G$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    contains a rainbow loose Hamilton cycle.\n                  <\/jats:p>","DOI":"10.1017\/s0963548325100266","type":"journal-article","created":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T11:47:14Z","timestamp":1762861634000},"page":"149-177","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["A rainbow Dirac theorem for loose Hamilton cycles in hypergraphs"],"prefix":"10.1017","volume":"35","author":[{"given":"Amarja","family":"Kathapurkar","sequence":"first","affiliation":[{"name":"University of Birmingham"}]},{"given":"Patrick","family":"Morris","sequence":"additional","affiliation":[{"name":"Universitat Polit\u00e8cnica de Catalunya (UPC)"}]},{"given":"Guillem","family":"Perarnau","sequence":"additional","affiliation":[{"name":"Universitat Polit\u00e8cnica de Catalunya (UPC)"},{"name":"Centre de Recerca Matem\u00e0tica"}]}],"member":"56","published-online":{"date-parts":[[2025,11,11]]},"reference":[{"key":"S0963548325100266_ref4","first-page":"P1","article-title":"Properly colored Hamilton cycles in Dirac-type hypergraphs","volume":"30","author":"Antoniuk","year":"2023","journal-title":"Electron. J. Comb."},{"key":"S0963548325100266_ref25","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1098-2418(199810\/12)13:3\/4<467::AID-RSA15>3.0.CO;2-W"},{"key":"S0963548325100266_ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2006.02.004"},{"key":"S0963548325100266_ref14","doi-asserted-by":"publisher","DOI":"10.1137\/18M1218881"},{"key":"S0963548325100266_ref38","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-24298-9_6"},{"key":"S0963548325100266_ref24","doi-asserted-by":"publisher","DOI":"10.1002\/9781118032718"},{"key":"S0963548325100266_ref26","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2010.11.013"},{"key":"S0963548325100266_ref19","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(91)90040-4"},{"key":"S0963548325100266_ref23","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2009.10.002"},{"key":"S0963548325100266_ref10","unstructured":"[10] Chakraborti, D. , Christoph, M. , Hunter, Z. , Montgomery, R. and Petrov, T. (2024) Almost-full transversals in equi-n-squares. arXiv preprint arXiv: 2412.07733."},{"key":"S0963548325100266_ref20","first-page":"495","article-title":"Une condition suffisante d\u2019existence d\u2019un circuit hamiltonien","volume":"251","author":"Ghouila-Houri","year":"1960","journal-title":"C. R. Acad. Sci. Paris"},{"key":"S0963548325100266_ref7","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107325708"},{"key":"S0963548325100266_ref1","doi-asserted-by":"publisher","DOI":"10.37236\/1204"},{"key":"S0963548325100266_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2019.105184"},{"key":"S0963548325100266_ref22","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(86)90038-5"},{"key":"S0963548325100266_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.procs.2023.08.229"},{"key":"S0963548325100266_ref33","unstructured":"[33] Ryser, H. J. (1967) Neuere probleme der kombinatorik. In Vortr\u00e4ge \u00fcber Kombinatorik, Oberwolfach, Vol. 69, 35. no. 91."},{"key":"S0963548325100266_ref11","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177729330"},{"key":"S0963548325100266_ref15","doi-asserted-by":"publisher","DOI":"10.1137\/16M1065732"},{"key":"S0963548325100266_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/s00208-008-0268-6"},{"key":"S0963548325100266_ref29","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-04016-0"},{"key":"S0963548325100266_ref5","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548311000253"},{"key":"S0963548325100266_ref31","doi-asserted-by":"publisher","DOI":"10.1090\/proc\/14220"},{"key":"S0963548325100266_ref36","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.3240010210"},{"key":"S0963548325100266_ref17","doi-asserted-by":"publisher","DOI":"10.37236\/2055"},{"key":"S0963548325100266_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.endm.2017.06.039"},{"key":"S0963548325100266_ref18","volume-title":"Some problems related to partitions of edges of a graph","author":"Erd\u0151s","year":"1983"},{"key":"S0963548325100266_ref35","doi-asserted-by":"publisher","DOI":"10.1017\/9781108332699.009"},{"key":"S0963548325100266_ref37","doi-asserted-by":"crossref","unstructured":"[37] Talagrand, M. (1995) Concentration of measure and isoperimetric inequalities in product spaces , Publications Math\u00e9matiques de l\u2019Institut des Hautes Etudes Scientifiques 81, 73\u2013205,10.1007\/BF02699376","DOI":"10.1007\/BF02699376"},{"key":"S0963548325100266_ref21","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20907"},{"key":"S0963548325100266_ref30","unstructured":"[30] Montgomery, R. (2023) A proof of the Ryser-Brualdi-Stein conjecture for large even n, arXiv preprint arXiv: 2310.19779."},{"key":"S0963548325100266_ref2","volume-title":"The probabilistic method","author":"Alon","year":"2016"},{"key":"S0963548325100266_ref13","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20835"},{"key":"S0963548325100266_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2013.07.004"},{"key":"S0963548325100266_ref16","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-2.1.69"},{"key":"S0963548325100266_ref32","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548305007042"},{"key":"S0963548325100266_ref34","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1975.59.567"},{"key":"S0963548325100266_ref27","doi-asserted-by":"publisher","DOI":"10.1007\/BF01196135"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548325100266","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,18]],"date-time":"2026-02-18T08:53:59Z","timestamp":1771404839000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548325100266\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,11]]},"references-count":38,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,3]]}},"alternative-id":["S0963548325100266"],"URL":"https:\/\/doi.org\/10.1017\/s0963548325100266","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,11]]},"assertion":[{"value":"\u00a9 The Author(s), 2025. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}