{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T15:42:54Z","timestamp":1777563774790,"version":"3.51.4"},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2018,7,16]],"date-time":"2018-07-16T00:00:00Z","timestamp":1531699200000},"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":[[2019,3]]},"abstract":"<jats:p>Let <jats:italic>k<\/jats:italic> \u2a7e 2 be an integer. We show that if <jats:italic>s<\/jats:italic> = 2 and <jats:italic>t<\/jats:italic> \u2a7e 2, or <jats:italic>s<\/jats:italic> = <jats:italic>t<\/jats:italic> = 3, then the maximum possible number of edges in a <jats:italic>C<\/jats:italic><jats:sub>2<jats:italic>k<\/jats:italic>+1<\/jats:sub>-free graph containing no induced copy of <jats:italic>K<jats:sub>s,t<\/jats:sub><\/jats:italic> is asymptotically equal to (<jats:italic>t<\/jats:italic> \u2212 <jats:italic>s<\/jats:italic> + 1)<jats:sup>1\/<jats:italic>s<\/jats:italic><\/jats:sup>(<jats:italic>n<\/jats:italic>\/2)<jats:sup>2\u22121\/<jats:italic>s<\/jats:italic><\/jats:sup> except when <jats:italic>k<\/jats:italic> = <jats:italic>s<\/jats:italic> = <jats:italic>t<\/jats:italic> = 2.<\/jats:p><jats:p>This strengthens a result of Allen, Keevash, Sudakov and Verstra\u00ebte [1], and answers a question of Loh, Tait, Timmons and Zhou [14].<\/jats:p>","DOI":"10.1017\/s0963548318000354","type":"journal-article","created":{"date-parts":[[2018,7,16]],"date-time":"2018-07-16T05:09:21Z","timestamp":1531717761000},"page":"241-252","source":"Crossref","is-referenced-by-count":5,"title":["Tur\u00e1n Number of an Induced Complete Bipartite Graph Plus an Odd Cycle"],"prefix":"10.1017","volume":"28","author":[{"given":"BEKA","family":"ERGEMLIDZE","sequence":"first","affiliation":[]},{"given":"ERVIN","family":"GY\u0150RI","sequence":"additional","affiliation":[]},{"given":"ABHISHEK","family":"METHUKU","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2018,7,16]]},"reference":[{"key":"S0963548318000354_ref14","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548317000542"},{"key":"S0963548318000354_ref10","doi-asserted-by":"publisher","DOI":"10.1006\/jcta.1996.0067"},{"key":"S0963548318000354_ref8","first-page":"215","article-title":"On a problem of graph theory","volume":"1","author":"Erd\u0151s","year":"1966","journal-title":"Stud Sci. Math. Hungar."},{"key":"S0963548318000354_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579234"},{"key":"S0963548318000354_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2014.01.007"},{"key":"S0963548318000354_ref5","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1966-036-2"},{"key":"S0963548318000354_ref2","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.1999.1906"},{"key":"S0963548318000354_ref3","first-page":"1244","article-title":"A H\u00f6lder type inequality for symmetric matrices with nonnegative entries","volume":"16","author":"Blakley","year":"1965","journal-title":"Proc. Amer. Math. Soc."},{"key":"S0963548318000354_ref9","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548300001814"},{"key":"S0963548318000354_ref11","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548311000629"},{"key":"S0963548318000354_ref13","doi-asserted-by":"publisher","DOI":"10.4064\/cm-3-1-50-57"},{"key":"S0963548318000354_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/BF02024498"},{"key":"S0963548318000354_ref4","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2007.08.016"},{"key":"S0963548318000354_ref12","doi-asserted-by":"publisher","DOI":"10.1007\/BF01261323"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548318000354","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,12]],"date-time":"2019-04-12T15:03:30Z","timestamp":1555081410000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548318000354\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,16]]},"references-count":14,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,3]]}},"alternative-id":["S0963548318000354"],"URL":"https:\/\/doi.org\/10.1017\/s0963548318000354","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,7,16]]}}}