{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:50:27Z","timestamp":1759063827970},"reference-count":8,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2006,10,6]],"date-time":"2006-10-06T00:00:00Z","timestamp":1160092800000},"content-version":"vor","delay-in-days":5818,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1990,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>C<\/jats:italic> be the class of triangle\u2010free graphs with maximum degree at most three. A lower bound for the number of edges in a graph of <jats:italic>C<\/jats:italic> is derived in terms of the number of vertices and the independence. Several classes of graphs for which this bound is attained are given. As corollaries, we obtain the best possible lower bound for the independence ratio of a graph in <jats:italic>C<\/jats:italic> and evaluate some Ramsey\u2010type numbers.<\/jats:p>","DOI":"10.1002\/jgt.3190140503","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T12:51:24Z","timestamp":1180183884000},"page":"525-535","source":"Crossref","is-referenced-by-count":19,"title":["Size and independence in triangle\u2010free graphs with maximum degree three"],"prefix":"10.1002","volume":"14","author":[{"given":"Kathryn Fraughnaugh","family":"Jones","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,6]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190070105"},{"key":"e_1_2_1_3_2","first-page":"269","article-title":"On the size of independent sets in graphs","volume":"21","author":"Fajtlowicz S.","year":"1978","journal-title":"Cong. Numerantium"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9800(68)80038-9"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(84)90058-3"},{"key":"e_1_2_1_6_2","first-page":"221","volume-title":"Graphs and Applications","author":"Jones K. F.","year":"1984"},{"key":"e_1_2_1_7_2","first-page":"219","article-title":"Maximum bipartite subgraphs and independence","volume":"48","author":"Jones K. F.","year":"1985","journal-title":"Cong. Numerantium"},{"key":"e_1_2_1_8_2","doi-asserted-by":"crossref","unstructured":"S. C.Locke Extremal properties of paths cycles andk\u2010colorable subgraphs of graphs. Ph.D. thesis University of Waterloo (1982).","DOI":"10.1002\/jgt.3190060206"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1979-0546922-6"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190140503","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190140503","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T19:05:59Z","timestamp":1698001559000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190140503"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,11]]},"references-count":8,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1990,11]]}},"alternative-id":["10.1002\/jgt.3190140503"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190140503","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,11]]}}}