{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:18:46Z","timestamp":1758824326963},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2018,5,9]],"date-time":"2018-05-09T00:00:00Z","timestamp":1525824000000},"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":[[2018,7]]},"abstract":"<jats:p>We study the minimum degree necessary to guarantee the existence of perfect and almost-perfect triangle-tilings in an <jats:italic>n<\/jats:italic>-vertex graph <jats:italic>G<\/jats:italic> with sublinear independence number. In this setting, we show that if \u03b4(<jats:italic>G<\/jats:italic>) \u2265 <jats:italic>n<\/jats:italic>\/3 + <jats:italic>o<\/jats:italic>(<jats:italic>n<\/jats:italic>), then <jats:italic>G<\/jats:italic> has a triangle-tiling covering all but at most four vertices. Also, for every <jats:italic>r<\/jats:italic> \u2265 5, we asymptotically determine the minimum degree threshold for a perfect triangle-tiling under the additional assumptions that <jats:italic>G<\/jats:italic> is <jats:italic>K<\/jats:italic><jats:sub><jats:italic>r<\/jats:italic><\/jats:sub>-free and <jats:italic>n<\/jats:italic> is divisible by 3.<\/jats:p>","DOI":"10.1017\/s0963548318000196","type":"journal-article","created":{"date-parts":[[2018,5,9]],"date-time":"2018-05-09T05:51:56Z","timestamp":1525845116000},"page":"449-474","source":"Crossref","is-referenced-by-count":8,"title":["Triangle-Tilings in Graphs Without Large Independent Sets"],"prefix":"10.1017","volume":"27","author":[{"given":"J\u00d3ZSEF","family":"BALOGH","sequence":"first","affiliation":[]},{"given":"ANDREW","family":"McDOWELL","sequence":"additional","affiliation":[]},{"given":"THEODORE","family":"MOLLA","sequence":"additional","affiliation":[]},{"given":"RICHARD","family":"MYCROFT","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2018,5,9]]},"reference":[{"key":"S0963548318000196_ref6","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1961-029-9"},{"key":"S0963548318000196_ref13","first-page":"33","article-title":"Asymptotic multipartite version of the Alon\u2013Yuster theorem","volume":"127","author":"Martin","year":"2013","journal-title":"J. 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