{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,12]],"date-time":"2023-11-12T05:04:14Z","timestamp":1699765454558},"reference-count":7,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,3]],"date-time":"2006-10-03T00:00:00Z","timestamp":1159833600000},"content-version":"vor","delay-in-days":8707,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1982,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Bounds are determined for the Ramsey number of the union of graphs versus a fixed graph <jats:italic>H<\/jats:italic>, based on the Ramsey number of the components versus <jats:italic>H<\/jats:italic>. For certain unions of graphs, the exact Ramsey number is determined. From these formulas, some new Ramsey numbers are indicated. In particular, if<jats:chem-struct-wrap><jats:chem-struct><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mimetype=\"image\/gif\" position=\"anchor\" specific-use=\"enlarged-web-image\" xlink:href=\"graphic\/must001.gif\"><jats:alt-text>magnified image<\/jats:alt-text><\/jats:graphic><\/jats:chem-struct><\/jats:chem-struct-wrap>.<\/jats:p><jats:p>Where <jats:italic>k<jats:sub>i<\/jats:sub><\/jats:italic> is the number of components of order <jats:italic>i<\/jats:italic> and <jats:italic>t<\/jats:italic><jats:sub>1<\/jats:sub> (<jats:italic>H<\/jats:italic>) is the minimum order of a color class over all critical colorings of the vertices of <jats:italic>H<\/jats:italic>, then<jats:chem-struct-wrap><jats:chem-struct><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mimetype=\"image\/gif\" position=\"anchor\" specific-use=\"enlarged-web-image\" xlink:href=\"graphic\/must002.gif\"><jats:alt-text>magnified image<\/jats:alt-text><\/jats:graphic><\/jats:chem-struct><\/jats:chem-struct-wrap>.<\/jats:p>","DOI":"10.1002\/jgt.3190060405","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T07:01:00Z","timestamp":1180422060000},"page":"413-417","source":"Crossref","is-referenced-by-count":2,"title":["Bounds for the ramsey number of a disconnected graph versus any graph"],"prefix":"10.1002","volume":"6","author":[{"given":"Ronald J.","family":"Gould","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael S.","family":"Jacobson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,3]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0095-8956(73)80005-X"},{"key":"e_1_2_1_3_2","first-page":"49","article-title":"On the color partitions of a graph","volume":"35","author":"Bouwsma W.","year":"1980","journal-title":"Elem. Math."},{"key":"e_1_2_1_4_2","unstructured":"S. A.Burr Ramsey numbers involving graphs with long suspended paths. Preprint."},{"key":"e_1_2_1_5_2","unstructured":"S. A.BurrandP.Erd\u00f6s Generalizations of a Ramsey\u2010theoretic result of Chv\u00e1tal. Preprint."},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190010118"},{"key":"e_1_2_1_7_2","unstructured":"M. S.Jacobson Ph. D. thesis Emory University (1980)."},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1975-069-0"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190060405","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190060405","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,12]],"date-time":"2023-11-12T03:55:09Z","timestamp":1699761309000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190060405"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,12]]},"references-count":7,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1982,12]]}},"alternative-id":["10.1002\/jgt.3190060405"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190060405","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,12]]}}}