{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T23:08:27Z","timestamp":1649113707633},"reference-count":17,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2016,6,21]],"date-time":"2016-06-21T00:00:00Z","timestamp":1466467200000},"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":[[2017,1]]},"abstract":"<jats:p>Let <jats:italic>D<jats:sub>k<\/jats:sub><\/jats:italic> denote the tournament on 3<jats:italic>k<\/jats:italic> vertices consisting of three disjoint vertex classes <jats:italic>V<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>V<\/jats:italic><jats:sub>2<\/jats:sub> and <jats:italic>V<\/jats:italic><jats:sub>3<\/jats:sub> of size <jats:italic>k<\/jats:italic>, each oriented as a transitive subtournament, and with edges directed from <jats:italic>V<\/jats:italic><jats:sub>1<\/jats:sub> to <jats:italic>V<\/jats:italic><jats:sub>2<\/jats:sub>, from <jats:italic>V<\/jats:italic><jats:sub>2<\/jats:sub> to <jats:italic>V<\/jats:italic><jats:sub>3<\/jats:sub> and from <jats:italic>V<\/jats:italic><jats:sub>3<\/jats:sub> to <jats:italic>V<\/jats:italic><jats:sub>1<\/jats:sub>. Fox and Sudakov proved that given a natural number <jats:italic>k<\/jats:italic> and \u03b5 &gt; 0, there is <jats:italic>n<\/jats:italic><jats:sub>0<\/jats:sub>(<jats:italic>k<\/jats:italic>, \u03b5) such that every tournament of order <jats:italic>n<\/jats:italic> \u2a7e <jats:italic>n<\/jats:italic><jats:sub>0<\/jats:sub>(<jats:italic>k<\/jats:italic>,\u03b5) which is \u03b5-far from being transitive contains <jats:italic>D<jats:sub>k<\/jats:sub><\/jats:italic> as a subtournament. Their proof showed that <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0963548316000213_inline1\" \/><jats:tex-math>$n_0(k,\\epsilon ) \\leq \\epsilon ^{-O(k\/\\epsilon ^2)}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and they conjectured that this could be reduced to <jats:italic>n<\/jats:italic><jats:sub>0<\/jats:sub>(<jats:italic>k<\/jats:italic>, \u03b5) \u2a7d \u03b5<jats:sup>\u2212<jats:italic>O<\/jats:italic>(<jats:italic>k<\/jats:italic>)<\/jats:sup>. Here we prove this conjecture.<\/jats:p>","DOI":"10.1017\/s0963548316000213","type":"journal-article","created":{"date-parts":[[2016,6,21]],"date-time":"2016-06-21T10:36:08Z","timestamp":1466505368000},"page":"68-77","source":"Crossref","is-referenced-by-count":1,"title":["Large Unavoidable Subtournaments"],"prefix":"10.1017","volume":"26","author":[{"given":"EOIN","family":"LONG","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,6,21]]},"reference":[{"key":"S0963548316000213_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2012.08.003"},{"key":"S0963548316000213_ref11","doi-asserted-by":"publisher","DOI":"10.1515\/9781400855162"},{"key":"S0963548316000213_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2008.04.003"},{"key":"S0963548316000213_ref15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2015.07.005"},{"key":"S0963548316000213_ref2","doi-asserted-by":"publisher","DOI":"10.1002\/9780470277331"},{"key":"S0963548316000213_ref4","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2009.170.941"},{"key":"S0963548316000213_ref6","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1947-08785-1"},{"key":"S0963548316000213_ref12","doi-asserted-by":"crossref","first-page":"50","DOI":"10.4064\/cm-3-1-50-57","article-title":"On a problem of K. 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