{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T09:08:41Z","timestamp":1768900121808,"version":"3.49.0"},"reference-count":7,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2011,2,3]],"date-time":"2011-02-03T00:00:00Z","timestamp":1296691200000},"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":[[2011,5]]},"abstract":"<jats:p>Szemer\u00e9di's Regularity Lemma is an important tool for analysing the structure of dense graphs. There are versions of the Regularity Lemma for sparse graphs, but these only apply when the graph satisfies some local density condition. In this paper, we prove a sparse Regularity Lemma that holds for all graphs. More generally, we give a Regularity Lemma that holds for arbitrary real matrices.<\/jats:p>","DOI":"10.1017\/s0963548310000490","type":"journal-article","created":{"date-parts":[[2011,2,3]],"date-time":"2011-02-03T06:17:42Z","timestamp":1296713862000},"page":"455-466","source":"Crossref","is-referenced-by-count":39,"title":["Szemer\u00e9di's Regularity Lemma for Matrices and Sparse Graphs"],"prefix":"10.1017","volume":"20","author":[{"given":"ALEXANDER","family":"SCOTT","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2011,2,3]]},"reference":[{"key":"S0963548310000490_ref5","first-page":"295","volume-title":"Combinatorics: Paul ErdH\u0151s is Eighty","author":"Koml\u00f3s","year":"1996"},{"key":"S0963548310000490_ref4","first-page":"289","volume-title":"Recent Advances in Algorithms and Combinatorics","author":"Kohayakawa","year":"2003"},{"key":"S0963548310000490_ref1","first-page":"211","volume-title":"Surveys in Combinatorics 2009","author":"Bollob\u00e1s","year":"2005"},{"key":"S0963548310000490_ref7","first-page":"399","volume-title":"Probl\u00e8mes Combinatoires et Th\u00e9orie des Graphes","author":"Szemer\u00e9di","year":"1978"},{"key":"S0963548310000490_ref6","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1098-2418(200005)16:3<260::AID-RSA3>3.0.CO;2-Q"},{"key":"S0963548310000490_ref2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511734885.010"},{"key":"S0963548310000490_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-60539-0_16"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548310000490","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T04:47:08Z","timestamp":1556340428000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548310000490\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,2,3]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2011,5]]}},"alternative-id":["S0963548310000490"],"URL":"https:\/\/doi.org\/10.1017\/s0963548310000490","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,2,3]]}}}