{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,30]],"date-time":"2025-04-30T04:05:32Z","timestamp":1745985932508,"version":"3.40.4"},"reference-count":30,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2025,1,27]],"date-time":"2025-01-27T00:00:00Z","timestamp":1737936000000},"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":[[2025,5]]},"abstract":"Abstract<\/jats:title>For a given graph \n$H$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, we say that a graph \n$G$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> has a perfect \n$H$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-subdivision tiling if \n$G$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> contains a collection of vertex-disjoint subdivisions of \n$H$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> covering all vertices of \n$G.$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> Let \n$\\delta _{\\mathrm {sub}}(n, H)$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> be the smallest integer \n$k$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> such that any \n$n$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-vertex graph \n$G$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> with minimum degree at least \n$k$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> has a perfect \n$H$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-subdivision tiling. For every graph \n$H$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, we asymptotically determined the value of \n$\\delta _{\\mathrm {sub}}(n, H)$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. More precisely, for every graph \n$H$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> with at least one edge, there is an integer \n$\\mathrm {hcf}_{\\xi }(H)$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and a constant \n$1 \\lt \\xi ^*(H)\\leq 2$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> that can be explicitly determined by structural properties of \n$H$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> such that \n$\\delta _{\\mathrm {sub}}(n, H) = \\left (1 - \\frac {1}{\\xi ^*(H)} + o(1) \\right )n$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> holds for all \n$n$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and \n$H$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> unless \n$\\mathrm {hcf}_{\\xi }(H) = 2$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and \n$n$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> is odd. When \n$\\mathrm {hcf}_{\\xi }(H) = 2$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and \n$n$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> is odd, then we show that \n$\\delta _{\\mathrm {sub}}(n, H) = \\left (\\frac {1}{2} + o(1) \\right )n$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p>","DOI":"10.1017\/s0963548324000452","type":"journal-article","created":{"date-parts":[[2025,1,27]],"date-time":"2025-01-27T07:56:53Z","timestamp":1737964613000},"page":"421-444","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["On perfect subdivision tilings"],"prefix":"10.1017","volume":"34","author":[{"given":"Hyunwoo","family":"Lee","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2025,1,27]]},"reference":[{"key":"S0963548324000452_ref26","first-page":"307","article-title":"Sur le nombre d\u2019absorption d\u2019un graphe simple. 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In Probl\u00e8mes combinatoires et th\u00e9ories des graphes (Colloques Internationaux du CNRS, University of Orsay, Orsay), Colloques Internationaux du CNRS, 260, CNRS, Paris, pp. 399\u2013401."},{"volume-title":"Studia Sci.","year":"1965","author":"Erd\u0151s","key":"S0963548324000452_ref7"},{"key":"S0963548324000452_ref21","first-page":"295","volume-title":"Combinatorics, Paul Erd\u0151s is Eighty","volume":"2","author":"Koml\u00f3s","year":"1993"},{"key":"S0963548324000452_ref16","doi-asserted-by":"publisher","DOI":"10.1090\/tran\/7411"},{"key":"S0963548324000452_ref2","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.1996.0020"},{"key":"S0963548324000452_ref14","doi-asserted-by":"publisher","DOI":"10.1137\/18M1197102"},{"key":"S0963548324000452_ref24","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2005.04.004"},{"key":"S0963548324000452_ref25","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-014-1410-8"},{"key":"S0963548324000452_ref28","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-13580-4_11"},{"key":"S0963548324000452_ref17","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/s004930070020","article-title":"Tiling Tur\u00e1n theorems","volume":"20","author":"Koml\u00f3s","year":"2000","journal-title":"Combinatorica"},{"key":"S0963548324000452_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01897150"},{"key":"S0963548324000452_ref18","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(00)00279-X"},{"key":"S0963548324000452_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2022.02.006"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548324000452","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,29]],"date-time":"2025-04-29T05:00:47Z","timestamp":1745902847000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548324000452\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,27]]},"references-count":30,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,5]]}},"alternative-id":["S0963548324000452"],"URL":"https:\/\/doi.org\/10.1017\/s0963548324000452","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"type":"print","value":"0963-5483"},{"type":"electronic","value":"1469-2163"}],"subject":[],"published":{"date-parts":[[2025,1,27]]},"assertion":[{"value":"\u00a9 The Author(s), 2025. 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