{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T18:37:32Z","timestamp":1648751852606},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2019,9,30]],"date-time":"2019-09-30T00:00:00Z","timestamp":1569801600000},"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":[[2020,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The induced removal lemma of Alon, Fischer, Krivelevich and Szegedy states that if an <jats:italic>n<\/jats:italic>-vertex graph <jats:italic>G<\/jats:italic> is <jats:italic>\u03b5<\/jats:italic>-far from being induced <jats:italic>H<\/jats:italic>-free then <jats:italic>G<\/jats:italic> contains <jats:italic>\u03b4<\/jats:italic><jats:sub><jats:italic>H<\/jats:italic><\/jats:sub>(<jats:italic>\u03b5<\/jats:italic>) \u00b7 <jats:italic>n<\/jats:italic><jats:sup><jats:italic>h<\/jats:italic><\/jats:sup> induced copies of <jats:italic>H<\/jats:italic>. Improving upon the original proof, Conlon and Fox proved that 1\/<jats:italic>\u03b4<\/jats:italic><jats:sub><jats:italic>H<\/jats:italic><\/jats:sub>(<jats:italic>\u03b5<\/jats:italic>)is at most a tower of height poly(1\/<jats:italic>\u03b5<\/jats:italic>), and asked if this bound can be further improved to a tower of height log(1\/<jats:italic>\u03b5<\/jats:italic>). In this paper we obtain such a bound for graphs <jats:italic>G<\/jats:italic> of density <jats:italic>O<\/jats:italic>(<jats:italic>\u03b5<\/jats:italic>). We actually prove a more general result, which, as a special case, also gives a new proof of Fox\u2019s bound for the (non-induced) removal lemma.<\/jats:p>","DOI":"10.1017\/s0963548319000233","type":"journal-article","created":{"date-parts":[[2019,10,1]],"date-time":"2019-10-01T02:30:56Z","timestamp":1569897056000},"page":"153-162","source":"Crossref","is-referenced-by-count":0,"title":["The Induced Removal Lemma in Sparse Graphs"],"prefix":"10.1017","volume":"29","author":[{"given":"Shachar","family":"Sapir","sequence":"first","affiliation":[]},{"given":"Asaf","family":"Shapira","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2019,9,30]]},"reference":[{"key":"S0963548319000233_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/BF01788085"},{"key":"S0963548319000233_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/PL00001621"},{"key":"S0963548319000233_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/s004930070001"},{"key":"S0963548319000233_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/s00039-012-0171-x"},{"key":"S0963548319000233_ref5","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539793247634"},{"key":"S0963548319000233_ref7","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2011.174.1.17"},{"key":"S0963548319000233_ref9","doi-asserted-by":"publisher","DOI":"10.1090\/tran\/7414"},{"key":"S0963548319000233_ref10","unstructured":"[10] Ruzsa, I. Z. and Szemer\u00e9di, E. (1978) Triple systems with no six points carrying three triangles. In Combinatorics (Keszthely, 1976), Vol. II, Vol. 18 of Colloquia Mathematica Societatis J\u00e1nos Bolyai, pp. 939\u2013945."},{"key":"S0963548319000233_ref4","first-page":"1","volume-title":"Surveys in Combinatorics 2013","author":"Conlon","year":"2013"},{"key":"S0963548319000233_ref1","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.1994.1005"},{"key":"S0963548319000233_ref11","unstructured":"[11] Szemer\u00e9di, E. (1978) Regular partitions of graphs. In Proc. Colloque Inter. CNRS, pp. 399\u2013401."}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548319000233","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,14]],"date-time":"2020-01-14T10:57:07Z","timestamp":1578999427000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548319000233\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,9,30]]},"references-count":11,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,1]]}},"alternative-id":["S0963548319000233"],"URL":"https:\/\/doi.org\/10.1017\/s0963548319000233","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,9,30]]}}}