{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,6]],"date-time":"2024-04-06T00:28:18Z","timestamp":1712363298779},"reference-count":17,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2014,1,14]],"date-time":"2014-01-14T00:00:00Z","timestamp":1389657600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[2014,12]]},"abstract":"Abstract<\/jats:title>Tutte's 3\u2010Flow Conjecture states that every 2\u2010edge\u2010connected graph with no 3\u2010cuts admits a 3\u2010flow. The 3\u2010Flow Conjecture is equivalent to the following: let G<\/jats:italic> be a 2\u2010edge\u2010connected graph, let S<\/jats:italic> be a set of at most three vertices of G<\/jats:italic>; if every 3\u2010cut of G<\/jats:italic> separates S<\/jats:italic> then G<\/jats:italic> has a 3\u2010flow. We show that minimum counterexamples to the latter statement are 3\u2010connected, cyclically 4\u2010connected, and cyclically 7\u2010edge\u2010connected.<\/jats:p>","DOI":"10.1002\/jgt.21785","type":"journal-article","created":{"date-parts":[[2014,1,14]],"date-time":"2014-01-14T16:27:42Z","timestamp":1389716862000},"page":"260-277","source":"Crossref","is-referenced-by-count":1,"title":["3\u2010Flows and Combs"],"prefix":"10.1002","volume":"77","author":[{"given":"C\u00e2ndida Nunes","family":"da Silva","sequence":"first","affiliation":[{"name":"CCTS FEDERAL UNIVERSITY OF S\u00c3O CARLOS \u2013 UFSCar SOROCABA SP BRAZIL"}]},{"given":"Cl\u00e1udio L.","family":"Lucchesi","sequence":"additional","affiliation":[{"name":"FACULTY OF COMPUTING FACOM\u2010UFMS CAMPO GRANDE MS BRAZIL"}]}],"member":"311","published-online":{"date-parts":[[2014,1,14]]},"reference":[{"key":"e_1_2_5_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84628-970-5"},{"key":"e_1_2_5_3_1","volume-title":"PhD thesis","author":"da Silva C. N.","year":"2009"},{"key":"e_1_2_5_4_1","unstructured":"C. N.da SilvaandC. L.Lucchesi 3\u2010Flows and minimal combs \u2013 supporting material Technical report facom\u2010ufms http:\/\/www.facom.ufms.br 2013."},{"key":"e_1_2_5_5_1","volume-title":"Master's thesis","author":"de Almeida e Silva L. M.","year":"1991"},{"key":"e_1_2_5_6_1","volume-title":"Graph Theory, volume 173 of Graduate Texts in Mathematics","author":"Diestel R.","year":"1996"},{"key":"e_1_2_5_7_1","first-page":"71","volume-title":"Selected Topics in Graph Theory","author":"Jaeger F.","year":"1988"},{"key":"e_1_2_5_8_1","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.2001.2054"},{"key":"e_1_2_5_9_1","doi-asserted-by":"publisher","DOI":"10.1006\/eujc.2001.0563"},{"key":"e_1_2_5_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0095-8956(03)00080-7"},{"key":"e_1_2_5_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2013.06.003"},{"key":"e_1_2_5_12_1","first-page":"289","volume-title":"Handbook of Combinatorics","author":"Seymour P. D.","year":"1995"},{"key":"e_1_2_5_13_1","first-page":"15","article-title":"Gr\u00f6tzsch's Theorem for the projective plane","volume":"28","author":"Steinberg R.","year":"1989","journal-title":"Ars Combinatoria"},{"key":"e_1_2_5_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0095-8956(03)00029-7"},{"key":"e_1_2_5_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2011.09.003"},{"key":"e_1_2_5_16_1","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1954-010-9"},{"key":"e_1_2_5_17_1","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190070307"},{"key":"e_1_2_5_18_1","volume-title":"Integer Flows and Cycle Covers of Graphs","author":"Zhang C.\u2010Q.","year":"1997"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.21785","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.21785","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,3]],"date-time":"2023-10-03T12:14:16Z","timestamp":1696335256000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.21785"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1,14]]},"references-count":17,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2014,12]]}},"alternative-id":["10.1002\/jgt.21785"],"URL":"https:\/\/doi.org\/10.1002\/jgt.21785","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1,14]]}}}