{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,12,14]],"date-time":"2023-12-14T17:38:38Z","timestamp":1702575518623},"reference-count":29,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2019,7,12]],"date-time":"2019-07-12T00:00:00Z","timestamp":1562889600000},"content-version":"am","delay-in-days":365,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#am"},{"start":{"date-parts":[[2018,7,12]],"date-time":"2018-07-12T00:00:00Z","timestamp":1531353600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100001807","name":"FAPESP","doi-asserted-by":"publisher","award":["2013\/03447\u20106"],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"CNPq","doi-asserted-by":"publisher","award":["310974\/2013\u20105","459335\/2014\u20106"],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS 1301698","DMS 1102086","1764385"],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Random Struct Algorithms"],"published-print":{"date-parts":[[2019,3]]},"abstract":"Abstract<\/jats:title>For graphs G<\/jats:italic> and F<\/jats:italic>, write if any coloring of the edges of G<\/jats:italic> with colors yields a monochromatic copy of the graph F<\/jats:italic>. Suppose is obtained from a graph S<\/jats:italic> with s<\/jats:italic> vertices and maximum degree d<\/jats:italic> by subdividing its edges h<\/jats:italic> times (that is, by replacing the edges of S<\/jats:italic> by paths of length h<\/jats:italic>\u2009+\u20091). We prove that there exists a graph G<\/jats:italic> with no more than edges for which holds, provided that . We also extend this result to the case in which Q<\/jats:italic> is a graph with maximum degree d<\/jats:italic> on q<\/jats:italic> vertices with the property that every pair of vertices of degree greater than 2 are distance at least h<\/jats:italic>\u2009+\u20091 apart. This complements work of Pak regarding the size Ramsey number of \u201clong subdivisions\u201d of bounded degree graphs.<\/jats:p>","DOI":"10.1002\/rsa.20783","type":"journal-article","created":{"date-parts":[[2018,7,13]],"date-time":"2018-07-13T05:06:57Z","timestamp":1531458417000},"page":"304-339","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["The size Ramsey number of short subdivisions of bounded degree graphs"],"prefix":"10.1002","volume":"54","author":[{"given":"Yoshiharu","family":"Kohayakawa","sequence":"first","affiliation":[{"name":"Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade de S\u00e3o Paulo 05508\u2010090 S\u00e3o Paulo Brazil"}]},{"given":"Troy","family":"Retter","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science Emory University Atlanta Georgia 30322"}]},{"given":"Vojt\u011bch","family":"R\u00f6dl","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science Emory University Atlanta Georgia 30322"}]}],"member":"311","published-online":{"date-parts":[[2018,7,12]]},"reference":[{"key":"e_1_2_11_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/1097-0118(200010)35:2<83::AID-JGT2>3.0.CO;2-V"},{"key":"e_1_2_11_3_1","first-page":"14","volume-title":"Universality and tolerance (extended abstract)","author":"Alon N.","year":"2000"},{"key":"e_1_2_11_4_1","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190070115"},{"key":"e_1_2_11_5_1","first-page":"34","volume-title":"On size Ramsey number of paths, trees and circuits, II, Mathematics of Ramsey Theory, Algorithms Combin","author":"Beck J.","year":"1990"},{"key":"e_1_2_11_6_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511814068"},{"key":"e_1_2_11_7_1","first-page":"49","volume-title":"Recent Developments in Graph Ramsey Theory, Surveys in combinatorics","author":"Conlon D.","year":"2015"},{"key":"e_1_2_11_8_1","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20363"},{"key":"e_1_2_11_9_1","doi-asserted-by":"publisher","DOI":"10.1017\/S096354831400056X"},{"key":"e_1_2_11_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579174"},{"key":"e_1_2_11_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02018930"},{"key":"e_1_2_11_12_1","unstructured":"R. J.FaudreeandR. H.Schelp A Survey of Results on the Size Ramsey Number Paul Erd\u0151s and his mathematics II (Budapest 1999) Bolyai Soc. Math. Stud. vol. 11 J\u00e1nos Bolyai Math. Soc. Budapest 2002 pp.291\u2013309."},{"key":"e_1_2_11_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579202"},{"key":"e_1_2_11_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2006.03.004"},{"key":"e_1_2_11_15_1","first-page":"227","volume-title":"The Sparse Regularity Lemma and Its Applications","author":"Gerke S.","year":"2005"},{"key":"e_1_2_11_16_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02808204"},{"key":"e_1_2_11_17_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548300001619"},{"key":"e_1_2_11_18_1","doi-asserted-by":"publisher","DOI":"10.1002\/9781118032718"},{"key":"e_1_2_11_19_1","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.3240040106"},{"key":"e_1_2_11_20_1","first-page":"216","volume-title":"Szemer\u00e9di's regularity lemma for sparse graphs, Foundations of Computational Mathematics (Rio de Janeiro, 1997)","author":"Kohayakawa Y.","year":"1997"},{"key":"e_1_2_11_21_1","first-page":"289","volume-title":"Szemer\u00e9di's regularity lemma and quasi\u2010randomness, Recent Advances in Algorithms and Combinatorics","author":"Kohayakawa Y.","year":"2003"},{"key":"e_1_2_11_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2011.01.004"},{"key":"e_1_2_11_23_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548315000279"},{"key":"e_1_2_11_24_1","unstructured":"I. Pak 2001"},{"key":"e_1_2_11_25_1","unstructured":"I.Pak Mixing time and long paths in graphs Proceedings of the 13th annual ACM\u2010SIAM Symposium on Discrete Algorithms (SODA 2002) 2002 pp.321\u2013328."},{"key":"e_1_2_11_26_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480101384086"},{"key":"e_1_2_11_27_1","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.10086"},{"key":"e_1_2_11_28_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(02)00396-5"},{"key":"e_1_2_11_29_1","doi-asserted-by":"publisher","DOI":"10.1007\/s004930070024"},{"key":"e_1_2_11_30_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548310000490"}],"container-title":["Random Structures & Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Frsa.20783","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/rsa.20783","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/rsa.20783","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/am-pdf\/10.1002\/rsa.20783","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/rsa.20783","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,14]],"date-time":"2023-09-14T01:04:12Z","timestamp":1694653452000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/rsa.20783"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,12]]},"references-count":29,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,3]]}},"alternative-id":["10.1002\/rsa.20783"],"URL":"https:\/\/doi.org\/10.1002\/rsa.20783","archive":["Portico"],"relation":{},"ISSN":["1042-9832","1098-2418"],"issn-type":[{"value":"1042-9832","type":"print"},{"value":"1098-2418","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,7,12]]},"assertion":[{"value":"2018-07-12","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}