{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,12,8]],"date-time":"2023-12-08T14:02:03Z","timestamp":1702044123653},"reference-count":25,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2020,12,11]],"date-time":"2020-12-11T00:00:00Z","timestamp":1607644800000},"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":[[2021,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove that, for any <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548320000577_inline1.png\" \/><jats:tex-math>$t \\ge 3$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, there exists a constant <jats:italic>c<\/jats:italic> = <jats:italic>c<\/jats:italic>(<jats:italic>t<\/jats:italic>) &gt; 0 such that any <jats:italic>d<\/jats:italic>-regular <jats:italic>n<\/jats:italic>-vertex graph with the second largest eigenvalue in absolute value \u03bb satisfying <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548320000577_inline2.png\" \/><jats:tex-math>$\\lambda \\le c{d^{t - 1}}\/{n^{t - 2}}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> contains vertex-disjoint copies of <jats:italic>k<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic><\/jats:sub> covering all but at most <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548320000577_inline3.png\" \/><jats:tex-math>${n^{1 - 1\/(8{t^4})}}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> vertices. This provides further support for the conjecture of Krivelevich, Sudakov and Sz\u00e1bo (<jats:italic>Combinatorica<\/jats:italic><jats:bold>24<\/jats:bold> (2004), pp. 403\u2013426) that (<jats:italic>n<\/jats:italic>, <jats:italic>d<\/jats:italic>, \u03bb)-graphs with <jats:italic>n<\/jats:italic> \u2208 3\u2115 and <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548320000577_inline4.png\" \/><jats:tex-math>$\\lambda \\le c{d^2}\/n$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> for a suitably small absolute constant <jats:italic>c<\/jats:italic> &gt; 0 contain triangle-factors. Our arguments combine tools from linear programming with probabilistic techniques, and apply them in a certain weighted setting. We expect this method will be applicable to other problems in the field.<\/jats:p>","DOI":"10.1017\/s0963548320000577","type":"journal-article","created":{"date-parts":[[2020,12,11]],"date-time":"2020-12-11T23:39:42Z","timestamp":1607729982000},"page":"570-590","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":2,"title":["Near-perfect clique-factors in sparse pseudorandom graphs"],"prefix":"10.1017","volume":"30","author":[{"given":"Jie","family":"Han","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yoshiharu","family":"Kohayakawa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yury","family":"Person","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2020,12,11]]},"reference":[{"key":"S0963548320000577_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2013.12.004"},{"key":"S0963548320000577_ref4","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(88)90189-6"},{"key":"S0963548320000577_ref1","unstructured":"[1] Allen, P. , B\u00f6ttcher, J. , H\u00e0n, H. , Kohayakawa, Y. and Person, Y. 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