{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T04:58:25Z","timestamp":1774155505518,"version":"3.50.1"},"reference-count":26,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2022,7,21]],"date-time":"2022-07-21T00:00:00Z","timestamp":1658361600000},"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":[[2023,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Given a graph <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548322000177_inline1.png\"\/><jats:tex-math>\n$H$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and a positive integer <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548322000177_inline2.png\"\/><jats:tex-math>\n$n$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, the <jats:italic>Tur\u00e1n number<\/jats:italic><jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548322000177_inline3.png\"\/><jats:tex-math>\n$\\mathrm{ex}(n,H)$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> is the maximum number of edges in an <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548322000177_inline4.png\"\/><jats:tex-math>\n$n$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-vertex graph that does not contain <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548322000177_inline5.png\"\/><jats:tex-math>\n$H$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> as a subgraph. A real number <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548322000177_inline6.png\"\/><jats:tex-math>\n$r\\in (1,2)$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> is called a <jats:italic>Tur\u00e1n exponent<\/jats:italic> if there exists a bipartite graph <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548322000177_inline7.png\"\/><jats:tex-math>\n$H$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> such that <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548322000177_inline8.png\"\/><jats:tex-math>\n$\\mathrm{ex}(n,H)=\\Theta (n^r)$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. A long-standing conjecture of Erd\u0151s and Simonovits states that <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548322000177_inline9.png\"\/><jats:tex-math>\n$1+\\frac{p}{q}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> is a Tur\u00e1n exponent for all positive integers <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548322000177_inline10.png\"\/><jats:tex-math>\n$p$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548322000177_inline11.png\"\/><jats:tex-math>\n$q$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> with <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548322000177_inline12.png\"\/><jats:tex-math>\n$q\\gt p$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p><jats:p>In this paper, we show that <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548322000177_inline13.png\"\/><jats:tex-math>\n$1+\\frac{p}{q}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> is a Tur\u00e1n exponent for all positive integers <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548322000177_inline14.png\"\/><jats:tex-math>\n$p$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548322000177_inline15.png\"\/><jats:tex-math>\n$q$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> with <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548322000177_inline16.png\"\/><jats:tex-math>\n$q \\gt p^{2}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. Our result also addresses a conjecture of Janzer [18].<\/jats:p>","DOI":"10.1017\/s0963548322000177","type":"journal-article","created":{"date-parts":[[2022,7,21]],"date-time":"2022-07-21T09:53:23Z","timestamp":1658397203000},"page":"134-150","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":3,"title":["Many Tur\u00e1n exponents via subdivisions"],"prefix":"10.1017","volume":"32","author":[{"given":"Tao","family":"Jiang","sequence":"first","affiliation":[]},{"given":"Yu","family":"Qiu","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2022,7,21]]},"reference":[{"key":"S0963548322000177_ref1","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548303005741"},{"key":"S0963548322000177_ref19","doi-asserted-by":"publisher","DOI":"10.1112\/blms.12404"},{"key":"S0963548322000177_ref22","doi-asserted-by":"publisher","DOI":"10.1137\/19M1265442"},{"key":"S0963548322000177_ref4","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1966-036-2"},{"key":"S0963548322000177_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579343"},{"key":"S0963548322000177_ref2","first-page":"939","article-title":"Random algebraic construction of extremal graphs","volume":"47","author":"Bukh","year":"2015","journal-title":"Bull. 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