{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T05:26:29Z","timestamp":1767245189047},"reference-count":29,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2013,8,8]],"date-time":"2013-08-08T00:00:00Z","timestamp":1375920000000},"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":[[2013,9]]},"abstract":"<jats:p>Let \u0394 \u2265 2 be a fixed integer. We show that the random graph<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0963548313000199_inline1\" \/><jats:tex-math>${\\mathcal{G}_{n,p}}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>with<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0963548313000199_inline2\" \/><jats:tex-math>$p\\gg (\\log n\/n)^{1\/\\Delta}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>is robust with respect to the containment of almost spanning bipartite graphs<jats:italic>H<\/jats:italic>with maximum degree \u0394 and sublinear bandwidth in the following sense: asymptotically almost surely, if an adversary deletes arbitrary edges from<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0963548313000199_inline1\" \/><jats:tex-math>${\\mathcal{G}_{n,p}}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>in such a way that each vertex loses less than half of its neighbours, then the resulting graph still contains a copy of all such<jats:italic>H<\/jats:italic>.<\/jats:p>","DOI":"10.1017\/s0963548313000199","type":"journal-article","created":{"date-parts":[[2013,8,8]],"date-time":"2013-08-08T09:27:31Z","timestamp":1375954051000},"page":"639-683","source":"Crossref","is-referenced-by-count":15,"title":["Almost Spanning Subgraphs of Random Graphs After Adversarial Edge Removal"],"prefix":"10.1017","volume":"22","author":[{"given":"JULIA","family":"B\u00d6TTCHER","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"YOSHIHARU","family":"KOHAYAKAWA","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ANUSCH","family":"TARAZ","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2013,8,8]]},"reference":[{"key":"S0963548313000199_ref14","first-page":"231","volume-title":"LATIN 2012","author":"Dellamonica","year":"2012"},{"key":"S0963548313000199_ref16","first-page":"54","volume-title":"Graphs and Other Combinatorial Topics: Prague 1982","author":"Erd\u0151s","year":"1983"},{"key":"S0963548313000199_ref3","unstructured":"Alon N. and Capalbo M. (2008) Optimal universal graphs with deterministic embedding. In Proc. 19th Annual ACM\u2013SIAM Symposium on Discrete Algorithms: SODA, pp. 373\u2013378."},{"key":"S0963548313000199_ref13","unstructured":"Dellamonica D. , Kohayakawa Y. , R\u00f6dl V. and Ruci\u0144ski A. (2008) Universality of random graphs. In Proc. 19th Annual ACM\u2013SIAM Symposium on Discrete Algorithms: SODA, pp. 782\u2013788."},{"key":"S0963548313000199_ref8","unstructured":"B\u00f6ttcher J. , Kohayakawa Y. and Taraz A. Almost spanning subgraphs of random graphs after adversarial edge removal. arXiv:1003.0890"},{"key":"S0963548313000199_ref7","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548311000642"},{"key":"S0963548313000199_ref29","first-page":"436","article-title":"Eine Extremalaufgabe aus der Graphentheorie.","volume":"48","author":"Tur\u00e1n","year":"1941","journal-title":"Mat. Fiz. Lapok"},{"key":"S0963548313000199_ref25","first-page":"289","volume-title":"Recent Advances in Algorithms and Combinatorics","author":"Kohayakawa","year":"2003"},{"key":"S0963548313000199_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-007-2182-z"},{"key":"S0963548313000199_ref26","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2011.01.004"},{"key":"S0963548313000199_ref9","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20383"},{"key":"S0963548313000199_ref1","doi-asserted-by":"crossref","first-page":"13","DOI":"10.37236\/1204","article-title":"Multicoloured Hamilton cycles","volume":"2","author":"Albert","year":"1995","journal-title":"Electron. J. Combin."},{"key":"S0963548313000199_ref24","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.10081"},{"key":"S0963548313000199_ref23","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-60539-0_16"},{"key":"S0963548313000199_ref6","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20345"},{"key":"S0963548313000199_ref21","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2011.03.002"},{"key":"S0963548313000199_ref20","first-page":"601","volume-title":"Combinatorial Theory and its Applications II: Balatonf\u00fcred 1969","author":"Hajnal","year":"1970"},{"key":"S0963548313000199_ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2009.10.010"},{"key":"S0963548313000199_ref28","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20235"},{"key":"S0963548313000199_ref17","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(93)90054-W"},{"key":"S0963548313000199_ref19","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(86)90038-5"},{"key":"S0963548313000199_ref4","doi-asserted-by":"crossref","unstructured":"Alon N. , Capalbo M. , Kohayakawa Y. , R\u00f6dl V. , Ruci\u0144ski A. and Szemer\u00e9di E. (2000) Universality and tolerance. In Proc. 41st Annual Symposium on Foundations of Computer Science: FOCS, pp. 14\u201321.","DOI":"10.1109\/SFCS.2000.892007"},{"key":"S0963548313000199_ref27","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548399003879"},{"key":"S0963548313000199_ref15","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-2.1.69"},{"key":"S0963548313000199_ref18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2006.03.004"},{"key":"S0963548313000199_ref12","doi-asserted-by":"crossref","first-page":"R32","DOI":"10.37236\/756","article-title":"On the resilience of long cycles in random graphs","volume":"15","author":"Dellamonica","year":"2008","journal-title":"Electron. J. Combin."},{"key":"S0963548313000199_ref22","doi-asserted-by":"publisher","DOI":"10.1002\/9781118032718"},{"key":"S0963548313000199_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/s00208-008-0268-6"},{"key":"S0963548313000199_ref2","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20143"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548313000199","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,1]],"date-time":"2020-08-01T16:43:19Z","timestamp":1596300199000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548313000199\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,8,8]]},"references-count":29,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2013,9]]}},"alternative-id":["S0963548313000199"],"URL":"https:\/\/doi.org\/10.1017\/s0963548313000199","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,8,8]]}}}