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Discrete Math."],"published-print":{"date-parts":[[2024,9,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We prove that for [Formula: see text] with [Formula: see text] and [Formula: see text], there exist [Formula: see text] and [Formula: see text] such that for every [Formula: see text], every [Formula: see text]-vertex graph [Formula: see text] with [Formula: see text] and [Formula: see text] contains an [Formula: see text]th power of a Hamilton cycle. We also show that the minimum degree condition is asymptotically sharp for [Formula: see text] and the [Formula: see text] case was recently conjectured by Staden and Treglown.<\/jats:p>","DOI":"10.1137\/24m163709x","type":"journal-article","created":{"date-parts":[[2024,9,16]],"date-time":"2024-09-16T04:01:16Z","timestamp":1726459276000},"page":"2489-2508","source":"Crossref","is-referenced-by-count":0,"title":["On Powers of Hamilton Cycles in Ramsey\u2013Tur\u00e1n Theory"],"prefix":"10.1137","volume":"38","author":[{"given":"Ming","family":"Chen","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2013-2962","authenticated-orcid":true,"given":"Jie","family":"Han","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics and Center for Applied Mathematics, Beijing Institute of Technology, Beijing, 100081, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yantao","family":"Tang","sequence":"additional","affiliation":[{"name":"Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan, 250100, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4992-6555","authenticated-orcid":true,"given":"Donglei","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mathematics, Shandong University, Jinan, 250100, China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,9,16]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20670"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2023.02.008"},{"key":"ref3","unstructured":"M. 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