{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,23]],"date-time":"2024-01-23T23:38:15Z","timestamp":1706053095087},"reference-count":7,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":3663,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2004,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove consistent, assuming there is a supercompact cardinal, that there is a singular strong limit cardinal<jats:italic>\u03bc<\/jats:italic>, of cofinality<jats:italic>\u03c9<\/jats:italic>, such that every<jats:italic>\u03bc<\/jats:italic><jats:sup>+<\/jats:sup>-chromatic graph<jats:italic>X<\/jats:italic>on<jats:italic>\u03bc<\/jats:italic><jats:sup>+<\/jats:sup>has an edge colouring<jats:italic>c<\/jats:italic>of<jats:italic>X<\/jats:italic>into<jats:italic>\u03bc<\/jats:italic>colours for which every vertex colouring<jats:italic>g<\/jats:italic>of<jats:italic>X<\/jats:italic>into at most<jats:italic>\u03bc<\/jats:italic>many colours has a<jats:italic>g<\/jats:italic>-colour class on which<jats:italic>c<\/jats:italic>takes every value.<\/jats:p><jats:p>The paper also contains some generalisations of the above statement in which<jats:italic>\u03bc<\/jats:italic><jats:sup>+<\/jats:sup>is replaced by other cardinals &gt;<jats:italic>\u03bc<\/jats:italic>.<\/jats:p>","DOI":"10.2178\/jsl\/1080938840","type":"journal-article","created":{"date-parts":[[2005,3,2]],"date-time":"2005-03-02T21:30:27Z","timestamp":1109799027000},"page":"255-264","source":"Crossref","is-referenced-by-count":0,"title":["Wild edge colourings of graphs"],"prefix":"10.1017","volume":"69","author":[{"given":"Mirna","family":"D\u017eamonja","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P\u00e9ter","family":"Komj\u00e1th","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Charles","family":"Morgan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S002248120000815X_ref002","first-page":"219","article-title":"Proof of a conjecture of P. Erd\u0151s","volume":"14","author":"Fodor","year":"1952","journal-title":"Acta Scientiarum Mathematicarum, Universitatis Szegediensis"},{"key":"S002248120000815X_ref001","first-page":"366","volume":"68","author":"D\u017eamonja","year":"2003","journal-title":"Universal graphs at the successor of a singular cardinal"},{"key":"S002248120000815X_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/BF02392561"},{"key":"S002248120000815X_ref006","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198537854.001.0001","volume-title":"Cardinal arithmetic","author":"Shelah","year":"1994"},{"key":"S002248120000815X_ref004","volume-title":"Paul Erd\u0151s and his mathematics","volume":"10","author":"Hajnal"},{"key":"S002248120000815X_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/BF02761175"},{"key":"S002248120000815X_ref003","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511623561"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248120000815X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,23]],"date-time":"2024-01-23T22:45:55Z","timestamp":1706049955000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248120000815X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,3]]},"references-count":7,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2004,3]]}},"alternative-id":["S002248120000815X"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1080938840","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,3]]}}}