{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T13:34:05Z","timestamp":1773322445064,"version":"3.50.1"},"reference-count":10,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2013,10,18]],"date-time":"2013-10-18T00:00:00Z","timestamp":1382054400000},"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":[[2014,1]]},"abstract":"<jats:p>Given an edge <jats:italic>colouring<\/jats:italic> of a graph with a set of <jats:italic>m colours<\/jats:italic>, we say that the graph is <jats:italic>exactly m-coloured<\/jats:italic> if each of the <jats:italic>colours<\/jats:italic> is used. We consider edge colourings of the complete graph on <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0963548313000503_inline1\"\/><jats:tex-math>$\\mathbb{N}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> with infinitely many colours and show that either one can find an exactly <jats:italic>m<\/jats:italic>-coloured complete subgraph for every natural number <jats:italic>m<\/jats:italic> or there exists an infinite subset <jats:italic>X<\/jats:italic> \u2282 <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0963548313000503_inline1\"\/><jats:tex-math>$\\mathbb{N}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> coloured in one of two canonical ways: either the colouring is injective on <jats:italic>X<\/jats:italic> or there exists a distinguished vertex <jats:italic>v<\/jats:italic> in <jats:italic>X<\/jats:italic> such that <jats:italic>X<\/jats:italic>\\{<jats:italic>v<\/jats:italic>} is 1-coloured and each edge between <jats:italic>v<\/jats:italic> and <jats:italic>X<\/jats:italic>\\{<jats:italic>v<\/jats:italic>} has a distinct colour (all different to the colour used on <jats:italic>X<\/jats:italic>\\{<jats:italic>v<\/jats:italic>}). This answers a question posed by Stacey and Weidl in 1999. The techniques that we develop also enable us to resolve some further questions about finding exactly <jats:italic>m<\/jats:italic>-coloured complete subgraphs in colourings with finitely many colours.<\/jats:p>","DOI":"10.1017\/s0963548313000503","type":"journal-article","created":{"date-parts":[[2013,10,18]],"date-time":"2013-10-18T06:44:07Z","timestamp":1382078647000},"page":"102-115","source":"Crossref","is-referenced-by-count":3,"title":["A Canonical Ramsey Theorem for Exactly <i>m<\/i>-Coloured Complete Subgraphs"],"prefix":"10.1017","volume":"23","author":[{"given":"TEERADEJ","family":"KITTIPASSORN","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"BHARGAV P.","family":"NARAYANAN","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2013,10,18]]},"reference":[{"key":"S0963548313000503_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-006-0013-2"},{"key":"S0963548313000503_ref9","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s2-30.1.264"},{"key":"S0963548313000503_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-008-2148-9"},{"key":"S0963548313000503_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-002-0002-z"},{"key":"S0963548313000503_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(94)90284-4"},{"key":"S0963548313000503_ref10","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.1998.1855"},{"key":"S0963548313000503_ref8","unstructured":"Narayanan B. P. (2013) Exactly m-coloured complete infinite subgraphs. Submitted. arxiv.org:1303.2997."},{"key":"S0963548313000503_ref1","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-25.4.249"},{"key":"S0963548313000503_ref3","volume-title":"Ramsey Theory","author":"Graham","year":"1980"},{"key":"S0963548313000503_ref5","doi-asserted-by":"publisher","DOI":"10.1112\/S0024610706022800"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548313000503","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,22]],"date-time":"2019-04-22T21:12:02Z","timestamp":1555967522000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548313000503\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,10,18]]},"references-count":10,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,1]]}},"alternative-id":["S0963548313000503"],"URL":"https:\/\/doi.org\/10.1017\/s0963548313000503","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,10,18]]}}}