{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T12:11:50Z","timestamp":1697976710432},"reference-count":7,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":6427,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1989,3]]},"abstract":"Abstract<\/jats:title>A collection of (simple) cycles in a graph is called fundamental<\/jats:italic> if they form a basis for the cycle space and if they can be ordered such that Cj<\/jats:sub>(C<\/jats:italic>1<\/jats:sub> U \u2026 U C<\/jats:italic>j<\/jats:italic>\u20101<\/jats:sub>) \u2260 \u00d8 for all j.<\/jats:italic> We characterize by excluded minors those graphs for which every cycle basis is fundamental. We also give a constructive characterization that leads to a (polynomial) algorithm for recognizing these graphs. In addition, this algorithm can be used to determine if a graph has a cycle basis that covers every edge two or more times. An equivalent dual characterization for the cutset space is also given.<\/jats:p>","DOI":"10.1002\/jgt.3190130115","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T12:16:38Z","timestamp":1180181798000},"page":"117-137","source":"Crossref","is-referenced-by-count":13,"title":["Is every cycle basis fundamental?"],"prefix":"10.1002","volume":"13","author":[{"given":"David","family":"Hartvigsen","sequence":"first","affiliation":[]},{"given":"Eitan","family":"Zemel","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(65)90125-3"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1002\/andp.18471481202"},{"key":"e_1_2_1_4_3","first-page":"4","volume":"5","year":"1958","journal-title":"Trans. Inst. Radio Engrs."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1137\/0112059"},{"key":"e_1_2_1_6_2","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1090\/S0002-9947-1932-1501641-2","article-title":"Non\u2010separable and planar graphs","volume":"34","author":"Whitney H.","year":"1932","journal-title":"Trans. Am. Math. Soc."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.2307\/2371182"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190130115","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190130115","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T16:52:23Z","timestamp":1697907143000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190130115"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,3]]},"references-count":7,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1989,3]]}},"alternative-id":["10.1002\/jgt.3190130115"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190130115","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,3]]}}}