{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:19:38Z","timestamp":1758824378120},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2008,9,12]],"date-time":"2008-09-12T00:00:00Z","timestamp":1221177600000},"content-version":"unspecified","delay-in-days":5947,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[1992,6]]},"abstract":"<jats:p>Suppose that each vertex of a graph independently chooses a colour uniformly from the set {1, \u2026, <jats:italic>k<\/jats:italic>}; and let <jats:italic>S<jats:sub>i<\/jats:sub><\/jats:italic> be the random set of vertices coloured <jats:italic>i<\/jats:italic>. Farr shows that the probability that each set <jats:italic>S<jats:sub>i<\/jats:sub><\/jats:italic> is stable (so that the colouring is proper) is at most the product of the <jats:italic>k<\/jats:italic> probabilities that the sets <jats:italic>S<jats:sub>i<\/jats:sub><\/jats:italic> separately are stable. We give here a simple proof of an extension of this result.<\/jats:p>","DOI":"10.1017\/s096354830000016x","type":"journal-article","created":{"date-parts":[[2008,9,12]],"date-time":"2008-09-12T11:20:14Z","timestamp":1221218414000},"page":"157-160","source":"Crossref","is-referenced-by-count":6,"title":["On a Correlation Inequality of Farr"],"prefix":"10.1017","volume":"1","author":[{"given":"Colin","family":"McDiarmid","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2008,9,12]]},"reference":[{"key":"S096354830000016X_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-68874-4_6"},{"key":"S096354830000016X_ref007","doi-asserted-by":"publisher","DOI":"10.2307\/1426466"},{"key":"S096354830000016X_ref005","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100034241"},{"key":"S096354830000016X_ref008","first-page":"9","article-title":"Some inequalities for random graphs and percolation","volume":"13","author":"McDiarmid","year":"1987","journal-title":"Notes from New York Academy of Science Graph Theory Day"},{"key":"S096354830000016X_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/BF00536201"},{"key":"S096354830000016X_ref002","volume-title":"Combinatorics, set systems, hypergraphs, families of vectors and combinatorial probability","author":"Bollob\u00e1s","year":"1986"},{"key":"S096354830000016X_ref003","unstructured":"[3] Farr G. E. (to appear) A correlation inequality involving stable set and chromatic polynomials, J. Combinatorial Theory B."},{"key":"S096354830000016X_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0120903"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S096354830000016X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T21:37:48Z","timestamp":1558042668000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S096354830000016X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,6]]},"references-count":8,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1992,6]]}},"alternative-id":["S096354830000016X"],"URL":"https:\/\/doi.org\/10.1017\/s096354830000016x","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,6]]}}}