{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:18:30Z","timestamp":1758824310221},"reference-count":11,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,6]],"date-time":"2006-11-06T00:00:00Z","timestamp":1162771200000},"content-version":"vor","delay-in-days":6094,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1990,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let \ud835\udcbb denote the family of simple undirected graphs on <jats:italic>v<\/jats:italic> vertices having <jats:italic>e<\/jats:italic> edges ((<jats:italic>v<\/jats:italic>, <jats:italic>e<\/jats:italic>)\u2010graphs) and <jats:italic>P<\/jats:italic>(<jats:italic>G<\/jats:italic>; \u03bb) be the chromatic polynomial of a graph <jats:italic>G.<\/jats:italic> For the given integers <jats:italic>v<\/jats:italic>, <jats:italic>e<\/jats:italic>, and \u03bb, let <jats:italic>f<\/jats:italic>(<jats:italic>v<\/jats:italic>, <jats:italic>e<\/jats:italic>, \u03bb) denote the greatest number of proper colorings in \u03bb or less colors that a (<jats:italic>v, e<\/jats:italic>)\u2010graph <jats:italic>G<\/jats:italic> can have, i.e., <jats:italic>f<\/jats:italic>(<jats:italic>v<\/jats:italic>, <jats:italic>e<\/jats:italic>, \u03bb) = max{<jats:italic>P<\/jats:italic>(<jats:italic>G<\/jats:italic>; \u03bb): <jats:italic>G<\/jats:italic> \u2208 \ud835\udcbb}. In this paper we determine some new upper bounds for <jats:italic>f<\/jats:italic>(<jats:italic>v<\/jats:italic>, <jats:italic>e<\/jats:italic>, \u03bb).<\/jats:p>","DOI":"10.1002\/jgt.3190140104","type":"journal-article","created":{"date-parts":[[2007,6,8]],"date-time":"2007-06-08T23:55:00Z","timestamp":1181346900000},"page":"25-29","source":"Crossref","is-referenced-by-count":11,"title":["New upper bounds for the greatest number of proper colorings of a (<i>V<\/i>,<i>E<\/i>)\u2010graph"],"prefix":"10.1002","volume":"14","author":[{"given":"Felix","family":"Lazebnik","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,6]]},"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","volume-title":"Extremal Graph Theory","author":"Bollobas G.","year":"1978"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190130207"},{"key":"e_1_2_1_6_2","article-title":"Some corollaries from a theorem of Whitney","author":"Lazebnik F.","journal-title":"Discrete Math."},{"key":"e_1_2_1_7_2","unstructured":"L.Lovasz Combinatorial Problems and Exercises. North\u2010Holland Amsterdam New York Oxford (1979)."},{"key":"e_1_2_1_8_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_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-7557-9_17"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1932-05460-X"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(84)90013-9"},{"key":"e_1_2_1_12_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.3190140104","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190140104","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T18:54:33Z","timestamp":1698000873000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190140104"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,3]]},"references-count":11,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1990,3]]}},"alternative-id":["10.1002\/jgt.3190140104"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190140104","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,3]]}}}