{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,1,11]],"date-time":"2023-01-11T09:31:13Z","timestamp":1673429473428},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2008,9,12]],"date-time":"2008-09-12T00:00:00Z","timestamp":1221177600000},"content-version":"unspecified","delay-in-days":5490,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[1993,9]]},"abstract":"<jats:p>We consider a simple randomised algorithm that seeks a weak 2-colouring of a hypergraph <jats:italic>H<\/jats:italic>; that is, it tries to 2-colour the points of <jats:italic>H<\/jats:italic> so that no edge is monochromatic. If <jats:italic>H<\/jats:italic> has a particular well-behaved form of such a colouring, then the method is successful within expected number of iterations <jats:italic>O<\/jats:italic>(<jats:italic>n<\/jats:italic><jats:sup>3<\/jats:sup>) when <jats:italic>H<\/jats:italic> has <jats:italic>n<\/jats:italic> points. In particular, when applied to a graph <jats:italic>G<\/jats:italic> with <jats:italic>n<\/jats:italic> nodes and chromatic number 3, the method yields a 2-colouring of the vertices such that no triangle is monochromatic in expected time <jats:italic>O<\/jats:italic>(<jats:italic>n<\/jats:italic><jats:sup>4<\/jats:sup>).<\/jats:p>","DOI":"10.1017\/s0963548300000730","type":"journal-article","created":{"date-parts":[[2008,9,12]],"date-time":"2008-09-12T11:18:58Z","timestamp":1221218338000},"page":"363-365","source":"Crossref","is-referenced-by-count":14,"title":["A Random Recolouring Method for Graphs and Hypergraphs"],"prefix":"10.1017","volume":"2","author":[{"given":"Colin","family":"McDiarmid","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2008,9,12]]},"reference":[{"key":"S0963548300000730_ref004","volume-title":"Computers and Intractability","author":"Garey","year":"1979"},{"key":"S0963548300000730_ref003","volume-title":"An Introduction to Probability Theory and its Applications","volume":"1","author":"Feller","year":"1968"},{"key":"S0963548300000730_ref002","first-page":"133","volume-title":"Graph Theory and Combinatorics, Proc. Conference in honour of Paul Erd\u0151os","author":"Donnelly","year":"1984"},{"key":"S0963548300000730_ref005","unstructured":"[5] Khanna S. , Linial N. and Safra S. (1993) On the hardness of approximating the chromatic number. (Manuscript.)"},{"key":"S0963548300000730_ref006","first-page":"3","volume-title":"Proc. 4th S.E. Conference on Combinatorics, Graph Theory and Computing","author":"Lov\u00e1sz","year":"1973"},{"key":"S0963548300000730_ref001","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100060989"},{"key":"S0963548300000730_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(89)90214-8"},{"key":"S0963548300000730_ref008","unstructured":"[8] \u017derovnik J. (1987) A randomised heuristical algorithm for graph colouring. Proc. 8th Yugoslav Seminar on Graph Theory, Novi Sad."}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548300000730","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,15]],"date-time":"2019-05-15T21:57:49Z","timestamp":1557957469000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548300000730\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,9]]},"references-count":8,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1993,9]]}},"alternative-id":["S0963548300000730"],"URL":"https:\/\/doi.org\/10.1017\/s0963548300000730","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,9]]}}}