{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:21:00Z","timestamp":1759335660867},"reference-count":7,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":4844,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1993,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We examine some properties of the 2\u2010variable greedoid polynomial <jats:italic>f<\/jats:italic>(<jats:italic>G\u00b7,t,z<\/jats:italic>) when <jats:italic>G<\/jats:italic> is the branching greedoid associated to a rooted graph or a rooted directed graph. For rooted digraphs, we show a factoring property of <jats:italic>f<\/jats:italic>(<jats:italic>G\u00b7,t,z<\/jats:italic>) determines whether or not the rooted digraph has a directed cycle. \u00a9 1993 John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/jgt.3190170316","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T13:17:14Z","timestamp":1180185434000},"page":"433-442","source":"Crossref","is-referenced-by-count":4,"title":["On the greedoid polynomial for rooted graphs and rooted digraphs"],"prefix":"10.1002","volume":"17","author":[{"given":"Elizabeth W.","family":"McMahon","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0196-8858(85)90021-1"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511662041.009"},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","unstructured":"T.Brylawski The Tutte polynomial part I: General theory. Revised from Matroid Theory and its Applications Proceedings of the Third International Mathematical Summer Centre Liguori Naples Italy (1980)125\u2013276.","DOI":"10.1007\/978-3-642-11110-5_3"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.2307\/2047815"},{"key":"e_1_2_1_6_2","doi-asserted-by":"crossref","unstructured":"B.KorteandL.Lovasz Mathematical structures underlying greedy algorithms. Fundamentals of Computation Theory Lecture Notes in Computer Science 117 (1981)205\u2013209.","DOI":"10.1007\/3-540-10854-8_22"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511629563.009"},{"key":"e_1_2_1_8_2","volume-title":"Graph Theory","author":"Tutte W. T.","year":"1984"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190170316","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190170316","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T12:09:16Z","timestamp":1698235756000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190170316"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,7]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1993,7]]}},"alternative-id":["10.1002\/jgt.3190170316"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190170316","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,7]]}}}