{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,27]],"date-time":"2023-10-27T12:40:20Z","timestamp":1698410420835},"reference-count":7,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":4721,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1993,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A graph with <jats:italic>n<\/jats:italic> vertices that contains no triangle and no 5\u2010cycle and minimum degree exceeding <jats:italic>n<\/jats:italic>\/4 contains an independent set with at least (3<jats:italic>n<\/jats:italic>)\/7 vertices. This is best possible. The proof proceeds by producing a homomorphism to the 7\u2010cycle and invoking the No Homomorphism Lemma. For <jats:italic>k<\/jats:italic> \u2265 4, a graph with <jats:italic>n<\/jats:italic> vertices, odd girth 2<jats:italic>k<\/jats:italic>+1, and minimum degree exceeding <jats:italic>n<\/jats:italic>\/(<jats:italic>k<\/jats:italic>+1) contains an independent set with at least <jats:italic>kn<\/jats:italic>\/(2<jats:italic>k<\/jats:italic>+1) vertices; however, we suspect this is not best possible. \u00a9 1993 John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/jgt.3190170503","type":"journal-article","created":{"date-parts":[[2007,6,7]],"date-time":"2007-06-07T18:23:52Z","timestamp":1181240632000},"page":"581-588","source":"Crossref","is-referenced-by-count":3,"title":["Independence and graph homomorphisms graph homomorphisms"],"prefix":"10.1002","volume":"17","author":[{"given":"Michael O.","family":"Albertson","sequence":"first","affiliation":[]},{"given":"Lily","family":"Chan","sequence":"additional","affiliation":[]},{"given":"Ruth","family":"Haas","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/B978-0-12-386870-1.50008-3","volume-title":"Discrete Algorithms and Complexity","author":"Albertson M. O.","year":"1987"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(85)90073-1"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(74)90133-2"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190140412"},{"key":"e_1_2_1_6_2","unstructured":"K. L.Collins personal communication."},{"key":"e_1_2_1_7_2","first-page":"89","article-title":"Odd cycles of specified lengths in non\u2010bipartite graphs","volume":"13","author":"H\u00e4ggkvist R.","year":"1982","journal-title":"Ann. Discrete Math."},{"key":"e_1_2_1_8_2","unstructured":"P.Hell XingxingYu andHuishanZhou Independence ratios of graph powers.Discrete Math.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.3190170503","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190170503","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T07:58:38Z","timestamp":1698307118000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190170503"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,11]]},"references-count":7,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1993,11]]}},"alternative-id":["10.1002\/jgt.3190170503"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190170503","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,11]]}}}