{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,5]],"date-time":"2024-04-05T19:30:02Z","timestamp":1712345402070},"reference-count":8,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":6335,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1989,6]]},"abstract":"Abstract<\/jats:title>Let F denote the family of simple undirected graphs on v<\/jats:italic> vertices having e<\/jats:italic> edges ((v, e<\/jats:italic>)\u2010graphs) and P<\/jats:italic>(\u03bb, G<\/jats:italic>) be the chromatic polynomial of a graph G<\/jats:italic>. For the given integers v<\/jats:italic>, e, \u0394, let f<\/jats:italic>(v, e, \u0394) denote the greatest number of proper colorings in \u0394 or less colors that a (v, e)\u2010graph G can have, i.e., f(v, e, \u0394) = max{P(\u0394, G): G \u2208 F}. In this paper we determine f(v, e<\/jats:italic>, 2) and describe all graphs G<\/jats:italic> for which P<\/jats:italic>(2, G<\/jats:italic>) = f<\/jats:italic>(v, e<\/jats:italic>, 2). For f<\/jats:italic>(v, e<\/jats:italic>, 3), a lower bound and an upper bound are found.<\/jats:p>","DOI":"10.1002\/jgt.3190130207","type":"journal-article","created":{"date-parts":[[2007,6,9]],"date-time":"2007-06-09T00:50:55Z","timestamp":1181350255000},"page":"203-214","source":"Crossref","is-referenced-by-count":17,"title":["On the greatest number of 2 and 3 colorings of a (v, e)\u2010graph"],"prefix":"10.1002","volume":"13","author":[{"given":"Felix","family":"Lazebnik","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(85)90044-6"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.2307\/1967597"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.21236\/AD0705364"},{"key":"e_1_2_1_5_2","first-page":"1301","article-title":"Le nombre maximal de colorations d'un graphe","volume":"272","author":"Tomescu I.","year":"1971","journal-title":"C.R. Acad Sci. Paris"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-7557-9_17"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(84)90013-9"},{"key":"e_1_2_1_8_2","volume-title":"Introduction to Graph Theory","author":"Wilson R. J.","year":"1985"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1972-010-7"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190130207","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190130207","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T13:32:45Z","timestamp":1697981565000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190130207"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,6]]},"references-count":8,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1989,6]]}},"alternative-id":["10.1002\/jgt.3190130207"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190130207","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,6]]}}}