{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T18:08:17Z","timestamp":1787508497790,"version":"build-2736575974"},"reference-count":20,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2013,7,9]],"date-time":"2013-07-09T00:00:00Z","timestamp":1373328000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2013,9]]},"abstract":"\n A perfect matching\n M<\/jats:italic>\n in an edge-coloured complete bipartite graph\n \n K\n n,n<\/jats:sub>\n <\/jats:italic>\n is rainbow if no pair of edges in\n M<\/jats:italic>\n have the same colour. We obtain asymptotic enumeration results for the number of rainbow perfect matchings in terms of the maximum number of occurrences of each colour. We also consider two natural models of random edge-colourings of\n \n K\n n,n<\/jats:sub>\n <\/jats:italic>\n and show that if the number of colours is at least\n n<\/jats:italic>\n , then there is with high probability a rainbow perfect matching. This in particular shows that almost every square matrix of order\n n<\/jats:italic>\n in which every entry appears\n n<\/jats:italic>\n times has a Latin transversal.\n <\/jats:p>","DOI":"10.1017\/s096354831300028x","type":"journal-article","created":{"date-parts":[[2013,7,9]],"date-time":"2013-07-09T08:04:32Z","timestamp":1373357072000},"page":"783-799","source":"Crossref","is-referenced-by-count":6,"title":["Rainbow Perfect Matchings in Complete Bipartite Graphs: Existence and Counting"],"prefix":"10.1017","volume":"22","author":[{"given":"GUILLEM","family":"PERARNAU","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"ORIOL","family":"SERRA","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2013,7,9]]},"reference":[{"key":"S096354831300028X_ref20","first-page":"169","article-title":"Transversals in Latin squares.","volume":"15","author":"Wanless","year":"2007","journal-title":"Quasigroups Related Systems"},{"key":"S096354831300028X_ref19","volume-title":"Computational Recreations in Mathematica","author":"Vardi","year":"1991"},{"key":"S096354831300028X_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-008-0789-5"},{"key":"S096354831300028X_ref15","first-page":"179","article-title":"Uniform generation of random Latin rectangles.","volume":"9","author":"McKay","year":"1991","journal-title":"J. Combin. Math. Combin. Comput."},{"key":"S096354831300028X_ref13","doi-asserted-by":"publisher","DOI":"10.1006\/jcta.1998.2947"},{"key":"S096354831300028X_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2008.01.002"},{"key":"S096354831300028X_ref1","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.10102"},{"key":"S096354831300028X_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-011-0040-6"},{"key":"S096354831300028X_ref16","first-page":"24","volume-title":"Vortr\u00e4ge \u00fcber Kombinatorik","author":"Ryser","year":"1967"},{"key":"S096354831300028X_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(91)90040-4"},{"key":"S096354831300028X_ref4","first-page":"10","article-title":"Deriving the number of \u2018good\u2019 permutations, with applications to cryptography.","volume":"5","author":"Cooper","year":"1999","journal-title":"Kibernet. Sistem. Anal."},{"key":"S096354831300028X_ref11","doi-asserted-by":"crossref","first-page":"N26","DOI":"10.37236\/475","article-title":"Rainbow matching in edge-colored graphs","volume":"17","author":"LeSaulnier","year":"2010","journal-title":"Electron. J. Combin."},{"key":"S096354831300028X_ref8","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1520-6610(1996)4:6<405::AID-JCD3>3.0.CO;2-J"},{"key":"S096354831300028X_ref3","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20216"},{"key":"S096354831300028X_ref12","unstructured":"Lu L. and Szekely L. A. (2009) A new asymptotic enumeration technique: the Lovasz Local Lemma. ArXiv e-prints."},{"key":"S096354831300028X_ref17","doi-asserted-by":"publisher","DOI":"10.2307\/2589472"},{"key":"S096354831300028X_ref9","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20146"},{"key":"S096354831300028X_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-006-0012-8"},{"key":"S096354831300028X_ref6","doi-asserted-by":"crossref","first-page":"R59","DOI":"10.37236\/783","article-title":"On rainbow trees and cycles","volume":"15","author":"Frieze","year":"2008","journal-title":"Electron. J. Combin."},{"key":"S096354831300028X_ref18","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1975.59.567"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S096354831300028X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,7,30]],"date-time":"2020-07-30T00:26:09Z","timestamp":1596068769000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S096354831300028X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,7,9]]},"references-count":20,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2013,9]]}},"alternative-id":["S096354831300028X"],"URL":"https:\/\/doi.org\/10.1017\/s096354831300028x","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,7,9]]}}}