{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T05:51:59Z","timestamp":1775022719778,"version":"3.50.1"},"reference-count":35,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2023,11,14]],"date-time":"2023-11-14T00:00:00Z","timestamp":1699920000000},"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":[[2024,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We show that for any <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000378_inline1.png\"\/><jats:tex-math>\n$\\varepsilon \\gt 0$\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=\"S0963548323000378_inline2.png\"\/><jats:tex-math>\n$\\Delta \\in \\mathbb{N}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, there exists <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000378_inline3.png\"\/><jats:tex-math>\n$\\alpha \\gt 0$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> such that for sufficiently large <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000378_inline4.png\"\/><jats:tex-math>\n$n$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, every <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000378_inline5.png\"\/><jats:tex-math>\n$n$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-vertex graph <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000378_inline6.png\"\/><jats:tex-math>\n$G$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> satisfying that <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000378_inline7.png\"\/><jats:tex-math>\n$\\delta (G)\\geq \\varepsilon n$\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=\"S0963548323000378_inline8.png\"\/><jats:tex-math>\n$e(X, Y)\\gt 0$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> for every pair of disjoint vertex sets <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000378_inline9.png\"\/><jats:tex-math>\n$X, Y\\subseteq V(G)$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> of size <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000378_inline10.png\"\/><jats:tex-math>\n$\\alpha n$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> contains all spanning trees with maximum degree at most <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000378_inline11.png\"\/><jats:tex-math>\n$\\Delta$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. This strengthens a result of B\u00f6ttcher, Han, Kohayakawa, Montgomery, Parczyk, and Person.<\/jats:p>","DOI":"10.1017\/s0963548323000378","type":"journal-article","created":{"date-parts":[[2023,11,14]],"date-time":"2023-11-14T08:09:47Z","timestamp":1699949387000},"page":"270-285","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":1,"title":["Spanning trees in graphs without large bipartite holes"],"prefix":"10.1017","volume":"33","author":[{"given":"Jie","family":"Han","sequence":"first","affiliation":[]},{"given":"Jie","family":"Hu","sequence":"additional","affiliation":[]},{"given":"Lidan","family":"Ping","sequence":"additional","affiliation":[]},{"given":"Guanghui","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Yi","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Donglei","family":"Yang","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2023,11,14]]},"reference":[{"key":"S0963548323000378_ref19","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(99)00324-6"},{"key":"S0963548323000378_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/s00208-008-0268-6"},{"key":"S0963548323000378_ref7","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-2.1.69"},{"key":"S0963548323000378_ref16","doi-asserted-by":"publisher","DOI":"10.1002\/1097-0118(200103)36:3<121::AID-JGT1000>3.0.CO;2-U"},{"key":"S0963548323000378_ref33","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.22114"},{"key":"S0963548323000378_ref23","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548398003502"},{"key":"S0963548323000378_ref9","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548322000086"},{"key":"S0963548323000378_ref8","doi-asserted-by":"publisher","DOI":"10.5817\/CZ.MUNI.EUROCOMB23-051"},{"key":"S0963548323000378_ref22","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2020.12.006"},{"key":"S0963548323000378_ref28","doi-asserted-by":"publisher","DOI":"10.1137\/15M1032910"},{"key":"S0963548323000378_ref2","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.10070"},{"key":"S0963548323000378_ref1","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20670"},{"key":"S0963548323000378_ref34","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2019.106793"},{"key":"S0963548323000378_ref13","doi-asserted-by":"publisher","DOI":"10.1090\/tran\/6999"},{"key":"S0963548323000378_ref26","first-page":"295","article-title":"Szemer\u00e9di\u2019s regularity lemma and its applications in graph theory","volume":"2","author":"Koml\u00f3s","year":"1996","journal-title":"Combinatorica"},{"key":"S0963548323000378_ref10","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0118(199908)31:4<275::AID-JGT2>3.0.CO;2-F"},{"key":"S0963548323000378_ref15","first-page":"1","article-title":"A Ramsey\u2013Tur\u00e1n theory for tilings in graphs","author":"Han","year":"2023","journal-title":"Random Struct. 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