{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,20]],"date-time":"2023-10-20T04:12:37Z","timestamp":1697775157442},"reference-count":10,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,10,3]],"date-time":"2006-10-03T00:00:00Z","timestamp":1159833600000},"content-version":"vor","delay-in-days":10351,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1978,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A graph <jats:italic>G<\/jats:italic> is co\u2010connected if both <jats:italic>G<\/jats:italic> and its complement <jats:italic>\u1e20<\/jats:italic> are connected and nontrivial. For two graphs <jats:italic>A<\/jats:italic> and <jats:italic>B<\/jats:italic>, the connected Ramsey number <jats:italic>r<\/jats:italic><jats:sub>c<\/jats:sub>(<jats:italic>A, B<\/jats:italic>) is the smallest integer <jats:italic>n<\/jats:italic> such that there exists a co\u2010connected graph of order <jats:italic>n<\/jats:italic>, and if <jats:italic>G<\/jats:italic> is a co\u2010connected graph on at least <jats:italic>n<\/jats:italic> vertices, then <jats:italic>A<\/jats:italic> \u2a7d <jats:italic>G<\/jats:italic> or <jats:italic>B<\/jats:italic> \u2a7d <jats:italic>\u1e20<\/jats:italic>. If neither <jats:italic>A<\/jats:italic> or <jats:italic>B<\/jats:italic> contains a bridge, then it is known that <jats:italic>r<\/jats:italic><jats:sub>c<\/jats:sub>(<jats:italic>A, B<\/jats:italic>) = <jats:italic>r<\/jats:italic>(<jats:italic>A, B<\/jats:italic>), where <jats:italic>r<\/jats:italic>(<jats:italic>A, B<\/jats:italic>) denotes the usual Ramsey number of <jats:italic>A<\/jats:italic> and <jats:italic>B<\/jats:italic>. In this paper <jats:italic>r<\/jats:italic><jats:sub>c<\/jats:sub>(<jats:italic>A, B<\/jats:italic>) is calculated for some pairs (<jats:italic>A, B<\/jats:italic>) when <jats:italic>r<\/jats:italic>(<jats:italic>A, B<\/jats:italic>) is known and at least one of the graphs <jats:italic>A<\/jats:italic> or <jats:italic>B<\/jats:italic> has a bridge. In particular, <jats:italic>r<\/jats:italic><jats:sub>c<\/jats:sub>(<jats:italic>A, B<\/jats:italic>) is calculated for <jats:italic>A<\/jats:italic> a path and <jats:italic>B<\/jats:italic> either a cycle, star, or complete graph, and for <jats:italic>A<\/jats:italic> a star and <jats:italic>B<\/jats:italic> a complete graph.<\/jats:p>","DOI":"10.1002\/jgt.3190020204","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T06:05:34Z","timestamp":1180418734000},"page":"119-128","source":"Crossref","is-referenced-by-count":2,"title":["Some connected ramsey numbers"],"prefix":"10.1002","volume":"2","author":[{"given":"R. J.","family":"Faudree","sequence":"first","affiliation":[]},{"given":"R. H.","family":"Schelp","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,3]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"37","volume-title":"Theory of Graphs","author":"Bos\u00e1k J.","year":"1969"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0066435"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190010118"},{"key":"e_1_2_1_5_2","unstructured":"R. J.FaudreeandR. H.Schelp Some problems in Ramsey theory. To appear."},{"key":"e_1_2_1_6_2","article-title":"Connected Ramsey numbers for paths and stars","author":"Faudree R. J.","journal-title":"Proceedings of the Fifth Hungarian Colloquium"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(74)90122-8"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.21236\/AD0705364"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0066430"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(74)90048-3"},{"key":"e_1_2_1_11_2","unstructured":"D. P.Sumner The connected Ramsey number. To appear."}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190020204","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190020204","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T10:15:21Z","timestamp":1697710521000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190020204"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1978,6]]},"references-count":10,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1978,6]]}},"alternative-id":["10.1002\/jgt.3190020204"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190020204","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1978,6]]}}}