{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T10:32:02Z","timestamp":1773829922416,"version":"3.50.1"},"reference-count":25,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2021,4,6]],"date-time":"2021-04-06T00:00:00Z","timestamp":1617667200000},"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":[[2021,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The size-Ramsey number of a graph <jats:italic>F<\/jats:italic> is the smallest number of edges in a graph <jats:italic>G<\/jats:italic> with the Ramsey property for <jats:italic>F<\/jats:italic>, that is, with the property that any 2-colouring of the edges of <jats:italic>G<\/jats:italic> contains a monochromatic copy of <jats:italic>F<\/jats:italic>. We prove that the size-Ramsey number of the grid graph on <jats:italic>n<\/jats:italic> \u00d7 <jats:italic>n<\/jats:italic> vertices is bounded from above by <jats:italic>n<\/jats:italic><jats:sup>3+o(1)<\/jats:sup>.<\/jats:p>","DOI":"10.1017\/s0963548320000322","type":"journal-article","created":{"date-parts":[[2021,4,6]],"date-time":"2021-04-06T13:45:54Z","timestamp":1617716754000},"page":"670-685","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":5,"title":["On the size-Ramsey number of grid graphs"],"prefix":"10.1017","volume":"30","author":[{"given":"Dennis","family":"Clemens","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Meysam","family":"Miralaei","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Damian","family":"Reding","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mathias","family":"Schacht","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":[[2021,4,6]]},"reference":[{"key":"S0963548320000322_ref20","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.10081"},{"key":"S0963548320000322_ref6","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.22432"},{"key":"S0963548320000322_ref5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511814068"},{"key":"S0963548320000322_ref14","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2006.03.004"},{"key":"S0963548320000322_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(88)90189-6"},{"key":"S0963548320000322_ref12","doi-asserted-by":"publisher","DOI":"10.1007\/BF02018930"},{"key":"S0963548320000322_ref3","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190070115"},{"key":"S0963548320000322_ref17","doi-asserted-by":"publisher","DOI":"10.1002\/9781118032718"},{"key":"S0963548320000322_ref16","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548300001619"},{"key":"S0963548320000322_ref1","unstructured":"[1] Allen, P. , B\u00f6ttcher, J. , H\u00e0n, H. , Kohayakawa, Y. and Person, Y. Blow-up lemmas for sparse graphs. Submitted."},{"key":"S0963548320000322_ref23","doi-asserted-by":"publisher","DOI":"10.1007\/BF02582932"},{"key":"S0963548320000322_ref7","unstructured":"[7] Conlon, D. and Nenadov, R. Size Ramsey numbers of triangle-free graphs with bounded degree. Preprint."},{"key":"S0963548320000322_ref22","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548315000279"},{"key":"S0963548320000322_ref18","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548319000221"},{"key":"S0963548320000322_ref19","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-60539-0_16"},{"key":"S0963548320000322_ref24","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1007\/s004930070024","article-title":"On size Ramsey numbers of graphs with bounded degree","volume":"20","author":"R\u00f6dl","year":"2000","journal-title":"Combinatorica"},{"key":"S0963548320000322_ref21","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2011.01.004"},{"key":"S0963548320000322_ref8","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20363"},{"key":"S0963548320000322_ref15","doi-asserted-by":"publisher","DOI":"10.1007\/BF02808204"},{"key":"S0963548320000322_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-72905-8_4"},{"key":"S0963548320000322_ref10","doi-asserted-by":"publisher","DOI":"10.1137\/16M1069717"},{"key":"S0963548320000322_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579174"},{"key":"S0963548320000322_ref9","doi-asserted-by":"publisher","DOI":"10.1017\/S096354831400056X"},{"key":"S0963548320000322_ref25","unstructured":"[25] Szemer\u00e9di, E. (1978) Regular partitions of graphs. In Probl\u00e8mes Combinatoires et Th\u00e9orie des Graphes, Vol. 260 of Colloq. Internat. CNRS, pp. 399\u2013401. CNRS."},{"key":"S0963548320000322_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579202"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548320000322","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,8,6]],"date-time":"2021-08-06T13:36:58Z","timestamp":1628257018000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548320000322\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,6]]},"references-count":25,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2021,9]]}},"alternative-id":["S0963548320000322"],"URL":"https:\/\/doi.org\/10.1017\/s0963548320000322","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,4,6]]},"assertion":[{"value":"\u00a9 The Author(s), 2021. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}