{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T09:09:35Z","timestamp":1763543375902,"version":"3.45.0"},"reference-count":15,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2025,8,11]],"date-time":"2025-08-11T00:00:00Z","timestamp":1754870400000},"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":[[2025,11]]},"abstract":"Abstract<\/jats:title>\n \n The Erd\u0151s-S\u00f3s Conjecture states that every graph with average degree exceeding\n \n \n \n $k-1$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n contains every tree with\n \n \n \n $k$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n edges as a subgraph. We prove that there are\n \n \n \n $\\delta \\gt 0$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n and\n \n \n \n $k_0\\in \\mathbb N$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n such that the conjecture holds for every tree\n \n \n \n $T$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n with\n \n \n \n $k \\ge k_0$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n edges and every graph\n \n \n \n $G$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n with\n \n \n \n $|V(G)| \\le (1+\\delta )|V(T)|$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n .\n <\/jats:p>","DOI":"10.1017\/s0963548325100084","type":"journal-article","created":{"date-parts":[[2025,8,11]],"date-time":"2025-08-11T05:42:41Z","timestamp":1754890961000},"page":"927-931","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["Embedding nearly spanning trees"],"prefix":"10.1017","volume":"34","author":[{"given":"Bruce","family":"Reed","sequence":"first","affiliation":[{"name":"Academica Sinica"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7922-6413","authenticated-orcid":false,"given":"Maya","family":"Stein","sequence":"additional","affiliation":[{"name":"University of Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2025,8,11]]},"reference":[{"key":"S0963548325100084_ref12","doi-asserted-by":"publisher","DOI":"10.1137\/18M118195X"},{"key":"S0963548325100084_ref14","first-page":"459","volume-title":"Discrete Mathematics and Applications, Springer Optimization and Its Applications","volume":"165","author":"Stein","year":"2021"},{"key":"S0963548325100084_ref10","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.22899"},{"key":"S0963548325100084_ref13","first-page":"229","article-title":"A note on the Erd\u0151s\u2013S\u00f3s conjecture for graphs without \n\n\n\n${C}_4$","volume":"70","author":"Sacl\u00e9","year":"1997","journal-title":"J. Comb. Theory (Series B)"},{"key":"S0963548325100084_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/BF02024498"},{"key":"S0963548325100084_ref6","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.22511"},{"key":"S0963548325100084_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(95)00207-D"},{"key":"S0963548325100084_ref1","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548320000528"},{"key":"S0963548325100084_ref15","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2023.103827"},{"key":"S0963548325100084_ref3","doi-asserted-by":"publisher","DOI":"10.4064\/cm-13-2-251-254"},{"key":"S0963548325100084_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-04016-0"},{"key":"S0963548325100084_ref9","unstructured":"[9] Pokrovskiy, A. (2024) Hyperstability in the Erd\u0151s-S\u00f3s conjecture Preprint 2024, arXiv: 2409.15191."},{"key":"S0963548325100084_ref7","doi-asserted-by":"publisher","DOI":"10.1002\/1097-0118(200103)36:3<121::AID-JGT1000>3.0.CO;2-U"},{"key":"S0963548325100084_ref11","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.22897"},{"key":"S0963548325100084_ref5","first-page":"P1","article-title":"On Erd\u0151s-S\u00f3s conjecture for trees of large size","volume":"23","author":"Goerlich","year":"2016","journal-title":"Electron. J. Comb."}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548325100084","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T09:04:46Z","timestamp":1763543086000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548325100084\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,11]]},"references-count":15,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2025,11]]}},"alternative-id":["S0963548325100084"],"URL":"https:\/\/doi.org\/10.1017\/s0963548325100084","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"type":"print","value":"0963-5483"},{"type":"electronic","value":"1469-2163"}],"subject":[],"published":{"date-parts":[[2025,8,11]]},"assertion":[{"value":"\u00a9 The Author(s), 2025. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}