{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T18:42:21Z","timestamp":1770835341757,"version":"3.50.1"},"reference-count":31,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2020,2,13]],"date-time":"2020-02-13T00:00:00Z","timestamp":1581552000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2020,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The theta graph <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548320000012_inline1.png\"\/><jats:tex-math>\n${\\Theta _{\\ell ,t}}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> consists of two vertices joined by <jats:italic>t<\/jats:italic> vertex-disjoint paths, each of length <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548320000012_inline2.png\"\/><jats:tex-math>\n$\\ell $\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. For fixed odd <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548320000012_inline3.png\"\/><jats:tex-math>\n$\\ell $\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and large <jats:italic>t<\/jats:italic>, we show that the largest graph not containing <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548320000012_inline4.png\"\/><jats:tex-math>\n${\\Theta _{\\ell ,t}}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> has at most <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548320000012_inline5.png\"\/><jats:tex-math>\n${c_\\ell }{t^{1 - 1\/\\ell }}{n^{1 + 1\/\\ell }}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> edges and that this is tight apart from the value of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548320000012_inline6.png\"\/><jats:tex-math>\n${c_\\ell }$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p>","DOI":"10.1017\/s0963548320000012","type":"journal-article","created":{"date-parts":[[2020,2,13]],"date-time":"2020-02-13T09:14:53Z","timestamp":1581585293000},"page":"495-507","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":17,"title":["Tur\u00e1n numbers of theta graphs"],"prefix":"10.1017","volume":"29","author":[{"given":"Boris","family":"Bukh","sequence":"first","affiliation":[]},{"given":"Michael","family":"Tait","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2020,2,13]]},"reference":[{"key":"S0963548320000012_ref5","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1966-036-2"},{"key":"S0963548320000012_ref18","doi-asserted-by":"publisher","DOI":"10.1006\/jcta.1996.0067"},{"key":"S0963548320000012_ref30","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(91)90097-4"},{"key":"S0963548320000012_ref16","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(83)90018-7"},{"key":"S0963548320000012_ref9","unstructured":"[9] Conlon, D. 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