{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T07:11:02Z","timestamp":1780384262955,"version":"3.54.1"},"reference-count":7,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,10,6]],"date-time":"2006-10-06T00:00:00Z","timestamp":1160092800000},"content-version":"vor","delay-in-days":4023,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1995,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For each <jats:italic>k<\/jats:italic> \u2265 3, we construct a finite directed strongly <jats:italic>k<\/jats:italic>\u2010connected graph <jats:italic>D<\/jats:italic> containing a vertex <jats:italic>t<\/jats:italic> with the following property: For any <jats:italic>k<\/jats:italic> spanning <jats:italic>t<\/jats:italic>\u2010branchings, <jats:italic>B<\/jats:italic><jats:sub>1<\/jats:sub>, \u2026, <jats:italic>B<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic><\/jats:sub> in <jats:italic>D<\/jats:italic> (i. e., each <jats:italic>B<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub> is a spanning tree in <jats:italic>D<\/jats:italic> directed toward <jats:italic>t<\/jats:italic>), there exists a vertex <jats:italic>x<\/jats:italic> \u2260 <jats:italic>t<\/jats:italic> of <jats:italic>D<\/jats:italic> such that the <jats:italic>k, x, t<\/jats:italic>\u2010paths in <jats:italic>B<\/jats:italic><jats:sub>1<\/jats:sub>, \u2026, <jats:italic>B<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic><\/jats:sub> are not pairwise openly disjoint. This disproves a well\u2010known conjecture of Frank. \u00a9 1995, John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/jgt.3190200212","type":"journal-article","created":{"date-parts":[[2007,6,7]],"date-time":"2007-06-07T16:22:16Z","timestamp":1181233336000},"page":"235-239","source":"Crossref","is-referenced-by-count":14,"title":["Disproof of a conjecture about independent branchings in <i>k<\/i>\u2010connected directed graphs"],"prefix":"10.1002","volume":"20","author":[{"given":"Andreas","family":"Huck","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2006,10,6]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(88)90015-6"},{"key":"e_1_2_1_3_2","first-page":"69","volume-title":"Combinatorial Structures and Their Applications","author":"Edmonds J.","year":"1969"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01202468"},{"key":"e_1_2_1_5_2","unstructured":"A.Huck Independent branchings in acyclic graphs. Submitted."},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(92)90230-S"},{"key":"e_1_2_1_7_2","volume-title":"Packing and Covering in Combinatorics","author":"Schrijver A.","year":"1979"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190110309"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190200212","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190200212","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T21:29:08Z","timestamp":1698355748000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190200212"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,10]]},"references-count":7,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1995,10]]}},"alternative-id":["10.1002\/jgt.3190200212"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190200212","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,10]]}}}