{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T04:59:08Z","timestamp":1698037148804},"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":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>D<jats:sub>1<\/jats:sub><\/jats:italic> and <jats:italic>D<\/jats:italic><jats:sub>2<\/jats:sub> be finite digraphs, both with vertex set <jats:italic>V<\/jats:italic>, let <jats:italic>a<\/jats:italic> and <jats:italic>b<\/jats:italic> be given functions from <jats:italic>V<\/jats:italic> to <jats:italic>Z<\/jats:italic>+, and let <jats:italic>k<\/jats:italic> be a positive integer. In this paper we give a necessary and sufficient condition for the existence of <jats:italic>k<\/jats:italic> arc\u2010disjoint arborescences in each of <jats:italic>D<jats:sub>1<\/jats:sub><\/jats:italic> and <jats:italic>D<jats:sub>2<\/jats:sub><\/jats:italic> satisfying the condition that for each <jats:italic>v<\/jats:italic> in <jats:italic>V<\/jats:italic><\/jats:p><jats:p><jats:chem-struct-wrap><jats:chem-struct><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mimetype=\"image\/gif\" position=\"anchor\" specific-use=\"enlarged-web-image\" xlink:href=\"graphic\/must001.gif\"><jats:alt-text>magnified image<\/jats:alt-text><\/jats:graphic><\/jats:chem-struct><\/jats:chem-struct-wrap> a<jats:italic>(v)<\/jats:italic> &lt;r<jats:sub>1<\/jats:sub><jats:italic>(v)<\/jats:italic> = r<jats:sub>2<\/jats:sub><jats:italic>(v)<\/jats:italic> &lt; b<jats:italic>(v).<\/jats:italic><\/jats:p><jats:p>Where r<jats:sub>i<\/jats:sub><jats:italic>(v)<\/jats:italic> denotes the number of the arborescences in D<jats:sub>i<\/jats:sub> rooted at v, i = 1, 2.<\/jats:p>","DOI":"10.1002\/jgt.3190130211","type":"journal-article","created":{"date-parts":[[2007,6,9]],"date-time":"2007-06-09T00:48:51Z","timestamp":1181350131000},"page":"249-256","source":"Crossref","is-referenced-by-count":2,"title":["Common root functions of two digraphs"],"prefix":"10.1002","volume":"13","author":[{"given":"Cai","family":"Mao\u2010cheng","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":"10.1002\/jgt.3190070213"},{"key":"e_1_2_1_3_2","first-page":"69","volume-title":"Proceedings of the International Conference on Combinatorics (Calgary)","author":"Edmonds J.","year":"1970"},{"key":"e_1_2_1_4_2","first-page":"91","volume-title":"Combinatorial Algorithms","author":"Edmonds J.","year":"1973"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-5060(08)70734-9"},{"key":"e_1_2_1_6_2","first-page":"189","article-title":"An algorithm for submodular functions on graphs","volume":"16","author":"Frank A.","year":"1982","journal-title":"Ann. Discrete Math."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-68874-4_10"},{"key":"e_1_2_1_8_2","first-page":"315","volume-title":"Progress in Combinatorial Optimization (Proceedings of the Silver Jubilee Conference on Combinatorics, University of Waterloo, 1982)","author":"Schrijver A.","year":"1984"},{"key":"e_1_2_1_9_2","volume-title":"Matroid Theory","author":"Welsh D. J. A.","year":"1976"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190130211","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190130211","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T13:32:26Z","timestamp":1697981546000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190130211"}},"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.3190130211"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190130211","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]]}}}