{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,5]],"date-time":"2024-08-05T11:57:52Z","timestamp":1722859072232},"reference-count":32,"publisher":"Cambridge University Press (CUP)","issue":"06","license":[{"start":{"date-parts":[[2019,7,9]],"date-time":"2019-07-09T00:00:00Z","timestamp":1562630400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2019,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Given two<jats:italic>k<\/jats:italic>-graphs (<jats:italic>k<\/jats:italic>-uniform hypergraphs)<jats:italic>F<\/jats:italic>and<jats:italic>H<\/jats:italic>, a perfect<jats:italic>F<\/jats:italic>-tiling (or<jats:italic>F<\/jats:italic>-factor) in<jats:italic>H<\/jats:italic>is a set of vertex-disjoint copies of<jats:italic>F<\/jats:italic>that together cover the vertex set of<jats:italic>H<\/jats:italic>. For all complete<jats:italic>k<\/jats:italic>-partite<jats:italic>k<\/jats:italic>-graphs<jats:italic>K<\/jats:italic>, Mycroft proved a minimum codegree condition that guarantees a<jats:italic>K<\/jats:italic>-factor in an<jats:italic>n<\/jats:italic>-vertex<jats:italic>k<\/jats:italic>-graph, which is tight up to an error term<jats:italic>o<\/jats:italic>(<jats:italic>n<\/jats:italic>). In this paper we improve the error term in Mycroft\u2019s result to a sublinear term that relates to the Tur\u00e1n number of<jats:italic>K<\/jats:italic>when the differences of the sizes of the vertex classes of<jats:italic>K<\/jats:italic>are co-prime. Furthermore, we find a construction which shows that our improved codegree condition is asymptotically tight in infinitely many cases, thus disproving a conjecture of Mycroft. Finally, we determine exact minimum codegree conditions for tiling<jats:italic>K<jats:sub>(k)<\/jats:sub><\/jats:italic>(1, \u2026 , 1, 2) and tiling loose cycles, thus generalizing the results of Czygrinow, DeBiasio and Nagle, and of Czygrinow, respectively.<\/jats:p>","DOI":"10.1017\/s096354831900021x","type":"journal-article","created":{"date-parts":[[2019,7,9]],"date-time":"2019-07-09T09:09:12Z","timestamp":1562663352000},"page":"840-870","source":"Crossref","is-referenced-by-count":3,"title":["Codegree Conditions for Tiling Complete k-Partite k-Graphs and Loose Cycles"],"prefix":"10.1017","volume":"28","author":[{"given":"Wei","family":"Gao","sequence":"first","affiliation":[]},{"given":"Jie","family":"Han","sequence":"additional","affiliation":[]},{"given":"Yi","family":"Zhao","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2019,7,9]]},"reference":[{"key":"S096354831900021X_ref34","author":"Zhao","year":"2015","journal-title":"Recent Trends in Combinatorics"},{"key":"S096354831900021X_ref20","volume":"233","author":"Keevash","year":"2015","journal-title":"A Geometric Theory for Hypergraph Matching"},{"key":"S096354831900021X_ref32","first-page":"399","volume-title":"Probl\u00e8mes Combinatoires et Th\u00e9orie des Graphes (Colloq. Internat. CNRS, Univ. Orsay, Orsay, 1976)","volume":"260","author":"Szemer\u00e9di","year":"1978"},{"key":"S096354831900021X_ref31","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548305007042"},{"key":"S096354831900021X_ref30","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-14444-8_16"},{"key":"S096354831900021X_ref18","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1002\/rsa.20362","volume":"39","author":"Keevash","year":"2011","journal-title":"Random Struct. Alg."},{"key":"S096354831900021X_ref17","doi-asserted-by":"publisher","DOI":"10.1112\/S0025579300006069"},{"key":"S096354831900021X_ref16","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.21833"},{"key":"S096354831900021X_ref15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2017.02.003"},{"key":"S096354831900021X_ref9","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548317000104"},{"key":"S096354831900021X_ref14","author":"Han","journal-title":"J. Combin. Theory Ser. B"},{"key":"S096354831900021X_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(85)90035-4"},{"key":"S096354831900021X_ref13","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548317000268"},{"key":"S096354831900021X_ref7","doi-asserted-by":"publisher","DOI":"10.4064\/aa-21-1-399-408"},{"key":"S096354831900021X_ref12","doi-asserted-by":"publisher","DOI":"10.1090\/tran\/6999"},{"key":"S096354831900021X_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/BF02759942"},{"key":"S096354831900021X_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2009.10.002"},{"key":"S096354831900021X_ref5","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.21726"},{"key":"S096354831900021X_ref10","first-page":"601","volume-title":"Combinatorial Theory and its Applications, II (Proc. Colloq., Balatonf\u00fcred, 1969)","author":"Hajnal","year":"1970"},{"key":"S096354831900021X_ref4","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.21998"},{"key":"S096354831900021X_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2013.07.004"},{"key":"S096354831900021X_ref1","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.1996.0020"},{"key":"S096354831900021X_ref29","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2015.09.007"},{"key":"S096354831900021X_ref28","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548301005028"},{"key":"S096354831900021X_ref27","doi-asserted-by":"crossref","first-page":"R63","DOI":"10.37236\/981","volume":"13","author":"Lu","year":"2007","journal-title":"Electron. J. Combin."},{"key":"S096354831900021X_ref26","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-014-1410-8"},{"key":"S096354831900021X_ref25","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2012.12.005"},{"key":"S096354831900021X_ref24","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-009-2254-3"},{"key":"S096354831900021X_ref23","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107325975.007"},{"key":"S096354831900021X_ref22","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2006.02.004"},{"key":"S096354831900021X_ref21","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(00)00279-X"},{"key":"S096354831900021X_ref33","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-10.1.79"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S096354831900021X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,20]],"date-time":"2024-07-20T19:28:44Z","timestamp":1721503724000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S096354831900021X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,9]]},"references-count":32,"journal-issue":{"issue":"06","published-print":{"date-parts":[[2019,11]]}},"alternative-id":["S096354831900021X"],"URL":"https:\/\/doi.org\/10.1017\/s096354831900021x","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,7,9]]}}}