{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T02:15:38Z","timestamp":1740104138093,"version":"3.37.3"},"reference-count":13,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2019,11,8]],"date-time":"2019-11-08T00:00:00Z","timestamp":1573171200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["283194"],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[2020,5]]},"abstract":"Abstract<\/jats:title>It is well known that in every \u2010coloring of the edges of the complete bipartite graph there is a monochromatic connected component with at least vertices. In this paper we study an extension of this problem by replacing complete bipartite graphs by bipartite graphs of large minimum degree. We conjecture that in every \u2010coloring of the edges of an \u2010bipartite graph with , and , there exists a monochromatic component on at least vertices (as in the complete bipartite graph). If true, the minimum degree condition is sharp (in that both inequalities cannot be made weak when and are divisible by ). We prove the conjecture for r<\/jats:italic>\u2009=\u20092 and we prove a weaker bound for all r<\/jats:italic>\u2009\u2265\u20093. As a corollary, we obtain a result about the existence of monochromatic components with at least n<\/jats:italic>\/(r<\/jats:italic>\u2009\u2212\u20091) vertices in r<\/jats:italic>\u2010colored graphs with large minimum degree.<\/jats:p>","DOI":"10.1002\/jgt.22510","type":"journal-article","created":{"date-parts":[[2019,11,8]],"date-time":"2019-11-08T13:16:47Z","timestamp":1573219007000},"page":"117-130","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Large monochromatic components in multicolored bipartite graphs"],"prefix":"10.1002","volume":"94","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7569-7952","authenticated-orcid":false,"given":"Louis","family":"DeBiasio","sequence":"first","affiliation":[{"name":"Department of Mathematics Miami University Oxford Ohio"}]},{"given":"Robert A.","family":"Krueger","sequence":"additional","affiliation":[{"name":"Department of Mathematics Miami University Oxford Ohio"}]},{"given":"G\u00e1bor N.","family":"S\u00e1rk\u00f6zy","sequence":"additional","affiliation":[{"name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics Hungarian Academy of Sciences Budapest Hungary"},{"name":"Computer Science Department Worcester Polytechnic Institute Worcester Massachusetts"}]}],"member":"311","published-online":{"date-parts":[[2019,11,8]]},"reference":[{"doi-asserted-by":"publisher","key":"e_1_2_6_2_1","DOI":"10.37236\/6089"},{"doi-asserted-by":"publisher","key":"e_1_2_6_3_1","DOI":"10.1137\/16M1069717"},{"doi-asserted-by":"publisher","key":"e_1_2_6_4_1","DOI":"10.1007\/978-0-8176-8092-3_5"},{"doi-asserted-by":"publisher","key":"e_1_2_6_5_1","DOI":"10.1016\/j.disc.2015.07.007"},{"key":"e_1_2_6_6_1","first-page":"62","article-title":"Partition coverings and blocking sets in hypergraphs (in Hungarian)","volume":"71","author":"Gy\u00e1rf\u00e1s A.","year":"1977","journal-title":"Commun. Comput. Autom. Inst. Hungar. Acad. Sci."},{"doi-asserted-by":"publisher","key":"e_1_2_6_7_1","DOI":"10.1017\/S0963548311000599"},{"doi-asserted-by":"publisher","key":"e_1_2_6_8_1","DOI":"10.37236\/7049"},{"doi-asserted-by":"publisher","key":"e_1_2_6_9_1","DOI":"10.1007\/s00373-008-0789-5"},{"doi-asserted-by":"publisher","key":"e_1_2_6_10_1","DOI":"10.1002\/(SICI)1098-2418(199805)12:3<297::AID-RSA5>3.0.CO;2-Q"},{"doi-asserted-by":"publisher","key":"e_1_2_6_11_1","DOI":"10.1002\/jgt.20365"},{"key":"e_1_2_6_12_1","first-page":"R41","article-title":"Generalizing the Ramsey problem through diameter","volume":"9","author":"Mubayi D.","year":"2002","journal-title":"Electron. J. Combin."},{"doi-asserted-by":"publisher","key":"e_1_2_6_13_1","DOI":"10.1016\/j.disc.2011.09.015"},{"unstructured":"E.Szemer\u00e9di Regular partitions of graphs Colloques Internationaux C.N.R.S. No. 260\u2014Probl\u00e8mes Combinatoires et Th\u00e9orie des Graphes Orsay Paris 1976 pp.\u00a0399\u2013401.","key":"e_1_2_6_14_1"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.22510","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.22510","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/jgt.22510","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.22510","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,6]],"date-time":"2023-09-06T16:23:15Z","timestamp":1694017395000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.22510"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,8]]},"references-count":13,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,5]]}},"alternative-id":["10.1002\/jgt.22510"],"URL":"https:\/\/doi.org\/10.1002\/jgt.22510","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"type":"print","value":"0364-9024"},{"type":"electronic","value":"1097-0118"}],"subject":[],"published":{"date-parts":[[2019,11,8]]},"assertion":[{"value":"2018-06-13","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-10-06","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-11-08","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}