{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,31]],"date-time":"2023-10-31T06:27:38Z","timestamp":1698733658190},"reference-count":10,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2010,5,13]],"date-time":"2010-05-13T00:00:00Z","timestamp":1273708800000},"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":[[2011,1]]},"abstract":"<jats:p>Consider a randomly oriented graph<jats:italic>G<\/jats:italic>= (<jats:italic>V, E<\/jats:italic>) and let<jats:italic>a<\/jats:italic>,<jats:italic>s<\/jats:italic>and<jats:italic>b<\/jats:italic>be three distinct vertices in<jats:italic>V<\/jats:italic>. We study the correlation between the events {<jats:italic>a<\/jats:italic>\u2192<jats:italic>s<\/jats:italic>} and {<jats:italic>s<\/jats:italic>\u2192<jats:italic>b<\/jats:italic>}. We show that, counter-intuitively, when<jats:italic>G<\/jats:italic>is the complete graph<jats:italic>K<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>,<jats:italic>n<\/jats:italic>\u2265 5, then the correlation is positive. (It is negative for<jats:italic>n<\/jats:italic>= 3 and zero for<jats:italic>n<\/jats:italic>= 4.) We briefly discuss and pose problems for the same question on other graphs.<\/jats:p>","DOI":"10.1017\/s0963548310000131","type":"journal-article","created":{"date-parts":[[2010,5,13]],"date-time":"2010-05-13T06:56:31Z","timestamp":1273733791000},"page":"1-9","source":"Crossref","is-referenced-by-count":4,"title":["A Counter-Intuitive Correlation in a Random Tournament"],"prefix":"10.1017","volume":"20","author":[{"given":"SVEN ERICK","family":"ALM","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"SVANTE","family":"LINUSSON","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2010,5,13]]},"reference":[{"key":"S0963548310000131_ref9","article-title":"On percolation and the bunkbed conjecture","volume":"XX","author":"Linusson","year":"2010","journal-title":"Combin. Probab. Comput."},{"key":"S0963548310000131_ref6","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.1007"},{"key":"S0963548310000131_ref7","volume-title":"Proc. FPSAC'03: Formal Power Series and Algebraic Combinatorics","author":"H\u00e4ggstr\u00f6m","year":"2003"},{"key":"S0963548310000131_ref4","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20102"},{"key":"S0963548310000131_ref8","unstructured":"[8] Linusson S. (2009) A note on correlations in randomly oriented graphs. Preprint. arXiv:0905.2881."},{"key":"S0963548310000131_ref3","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1214\/aop\/1008956324","article-title":"A correlation inequality for connection events in percolation.","volume":"29","author":"van den Berg","year":"2001","journal-title":"Ann. Probab."},{"key":"S0963548310000131_ref10","doi-asserted-by":"publisher","DOI":"10.2307\/1426466"},{"key":"S0963548310000131_ref1","unstructured":"[1] Alm S. E. and Linusson S. A counter-intuitive correlation in a random tournament (early version of the present paper). arXiv:0906.0240"},{"key":"S0963548310000131_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-03981-6"},{"key":"S0963548310000131_ref2","unstructured":"[2] Alm S. E. and Linusson S. (2009) Correlations for paths in random orientations of G(n, p). Preprint. arXiv:0906.0720"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548310000131","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,4]],"date-time":"2020-06-04T15:54:25Z","timestamp":1591286065000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548310000131\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,5,13]]},"references-count":10,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,1]]}},"alternative-id":["S0963548310000131"],"URL":"https:\/\/doi.org\/10.1017\/s0963548310000131","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,5,13]]}}}