{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,1]],"date-time":"2025-12-01T02:45:54Z","timestamp":1764557154595},"reference-count":17,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,10,3]],"date-time":"2006-10-03T00:00:00Z","timestamp":1159833600000},"content-version":"vor","delay-in-days":8525,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1983,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We consider a random <jats:italic>m<\/jats:italic> by <jats:italic>n<\/jats:italic> bipartite tournament T<jats:sub>mn<\/jats:sub> consisting of <jats:italic>mn<\/jats:italic> independent random arcs which have a common probability <jats:italic>p<\/jats:italic> of being directed from the <jats:italic>m<\/jats:italic> part to the <jats:italic>n<\/jats:italic> part. We determine the expected value and variance of the number of 4\u2010cycles in <jats:italic>T<jats:sub>mn<\/jats:sub><\/jats:italic> and the probability that <jats:italic>T<jats:sub>mn<\/jats:sub><\/jats:italic> has no cycles. An asymptotic expression for this probability is also given when <jats:italic>p<\/jats:italic> = 1\/2 and <jats:italic>m<\/jats:italic> and <jats:italic>n<\/jats:italic> tend to infinity.<\/jats:p>","DOI":"10.1002\/jgt.3190070207","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T07:05:54Z","timestamp":1180422354000},"page":"183-194","source":"Crossref","is-referenced-by-count":4,"title":["On 4\u2010cycles in random bipartite tournaments"],"prefix":"10.1002","volume":"7","author":[{"given":"B\u00e9la","family":"Bollob\u00e9s","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ove","family":"Frank","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Micha\u0142","family":"Karo\u0144Ski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,3]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"The Theory of Partitions","author":"Andrews G.","year":"1976"},{"key":"e_1_2_1_3_2","first-page":"121","article-title":"A probability distribution connected with Stirling's second class numbers","volume":"34","author":"Arfwedson G.","year":"1951","journal-title":"Skand. 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Math. Hungar."}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190070207","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190070207","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,26]],"date-time":"2023-09-26T23:28:30Z","timestamp":1695770910000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190070207"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1983,6]]},"references-count":17,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1983,6]]}},"alternative-id":["10.1002\/jgt.3190070207"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190070207","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1983,6]]}}}