{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,18]],"date-time":"2026-05-18T17:49:25Z","timestamp":1779126565640,"version":"3.51.4"},"reference-count":5,"publisher":"Cambridge University Press (CUP)","issue":"1-2","license":[{"start":{"date-parts":[[2012,2,2]],"date-time":"2012-02-02T00:00:00Z","timestamp":1328140800000},"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":[[2012,3]]},"abstract":"<jats:p>A<jats:italic>rainbow subgraph<\/jats:italic>of an edge-coloured graph is a subgraph whose edges have distinct colours. The<jats:italic>colour degree<\/jats:italic>of a vertex<jats:italic>v<\/jats:italic>is the number of different colours on edges incident with<jats:italic>v<\/jats:italic>. Wang and Li conjectured that for<jats:italic>k<\/jats:italic>\u2265 4, every edge-coloured graph with minimum colour degree<jats:italic>k<\/jats:italic>contains a rainbow matching of size at least \u2308<jats:italic>k<\/jats:italic>\/2\u2309. A properly edge-coloured<jats:italic>K<\/jats:italic><jats:sub>4<\/jats:sub>has no such matching, which motivates the restriction<jats:italic>k<\/jats:italic>\u2265 4, but Li and Xu proved the conjecture for all other properly coloured complete graphs. LeSaulnier, Stocker, Wenger and West showed that a rainbow matching of size \u230a<jats:italic>k<\/jats:italic>\/2\u230b is guaranteed to exist, and they proved several sufficient conditions for a matching of size \u2308<jats:italic>k<\/jats:italic>\/2\u2309. We prove the conjecture in full.<\/jats:p>","DOI":"10.1017\/s0963548311000605","type":"journal-article","created":{"date-parts":[[2012,3,19]],"date-time":"2012-03-19T15:20:59Z","timestamp":1332170459000},"page":"255-263","source":"Crossref","is-referenced-by-count":21,"title":["Large Rainbow Matchings in Edge-Coloured Graphs"],"prefix":"10.1017","volume":"21","author":[{"given":"ALEXANDR","family":"KOSTOCHKA","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MATTHEW","family":"YANCEY","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2012,2,2]]},"reference":[{"key":"S0963548311000605_ref4","unstructured":"[4] Li X. and Xu Z. (2007) On the existence of a rainbow 1-factor in proper coloring of Krn (r). arXiv:0711.2847 [math.CO]."},{"key":"S0963548311000605_ref3","first-page":"145","article-title":"Color degree and heterochromatic matchings in edge-colored bipartite graphs","volume":"77","author":"Li","year":"2008","journal-title":"Util. Math."},{"key":"S0963548311000605_ref5","doi-asserted-by":"crossref","first-page":"R138","DOI":"10.37236\/862","article-title":"Heterochromatic matchings in edge-colored graphs","volume":"15","author":"Wang","year":"2008","journal-title":"Electron. J. Combin."},{"key":"S0963548311000605_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-008-0789-5"},{"key":"S0963548311000605_ref2","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."}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548311000605","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,7,4]],"date-time":"2020-07-04T12:49:08Z","timestamp":1593866948000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548311000605\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,2,2]]},"references-count":5,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2012,3]]}},"alternative-id":["S0963548311000605"],"URL":"https:\/\/doi.org\/10.1017\/s0963548311000605","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,2,2]]}}}