{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T21:25:08Z","timestamp":1698355508370},"reference-count":24,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":6243,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1989,9]]},"abstract":"Abstract<\/jats:title>Let O<\/jats:italic>(G<\/jats:italic>) denote the set of odd\u2010degree vertices of a graph G<\/jats:italic>. Let t<\/jats:italic> \u03f5 N and let \ud835\udcaet<\/jats:sub> denote the family of graphs G<\/jats:italic> whose edge set has a partition.<\/jats:p>E(g) = E1<\/jats:sub> U E2<\/jats:sub> U \u2026 U Et<\/jats:sub>such that O<\/jats:italic>(G<\/jats:italic>) = O<\/jats:italic>(G<\/jats:italic>[E<\/jats:italic>i<\/jats:sub>]) (1 \u2a7d i<\/jats:italic> \u2a7d t<\/jats:italic>). This partition is associated with a double cycle cover of G<\/jats:italic>. We show that if a graph G<\/jats:italic> is at most 5 edges short of being 4\u2010edge\u2010connected, then exactly one of these holds: G<\/jats:italic> \u03f5 \ud835\udcae3<\/jats:sub>, G<\/jats:italic> has at least one cut\u2010edge, or G<\/jats:italic> is contractible to the Petersen graph. We also improve a sufficient condition of Jaeger for G<\/jats:italic> \u03f5 \ud835\udcae2p<\/jats:italic>+1<\/jats:sub>(p<\/jats:italic> \u03f5 N).<\/jats:p>","DOI":"10.1002\/jgt.3190130408","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T12:24:59Z","timestamp":1180182299000},"page":"465-483","source":"Crossref","is-referenced-by-count":31,"title":["Double cycle covers and the petersen graph"],"prefix":"10.1002","volume":"13","author":[{"given":"Paul A.","family":"Catlin","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"B.AlspachandC.\u2010Q.Zhang Cycle coverings of graphs. Submitted."},{"key":"e_1_2_1_3_2","first-page":"31","article-title":"Problem ceteriju boja (The problem of four colors). Hrvatsko Prirodoslovno Dru\u0161tvo Glasnik Mat.\u2010Fiz","volume":"1","author":"Blanu\u0161a D.","year":"1946","journal-title":"Astr. Ser II"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190120105"},{"key":"e_1_2_1_6_2","unstructured":"P. A.Catlin The reduction of graph families closed under contraction. Submitted."},{"key":"e_1_2_1_7_2","unstructured":"P. A.Catlin Supereulerian graphs. Proceedings of the 250th Anniversary Conference. Congressus Numerantium 64 (1988)59\u201372."},{"key":"e_1_2_1_8_2","unstructured":"P. A.Catlin Four operations on families of graphs. Submitted."},{"key":"e_1_2_1_9_2","series-title":"Proceedings of the Sixth Quadrennial Conference of Graph Theory","volume-title":"Spanning trails joining two given edges","author":"Catlin P. A.","year":"1988"},{"key":"e_1_2_1_10_2","unstructured":"U.Celmins On cubic graphs that do not have an edge 3\u2010coloring. Ph.D. thesis University of Waterloo (1984)."},{"key":"e_1_2_1_11_2","first-page":"13","article-title":"A girth requirement for the double cycle cover conjecture","volume":"27","author":"Goddyn L.","year":"1985","journal-title":"Ann. Discrete Math."},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(83)90031-5"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190030110"},{"key":"e_1_2_1_14_2","doi-asserted-by":"crossref","unstructured":"F.Jaeger On circular flows in graphs. Colloquia Mathametica Societatis J\u00e1nos Bolyai Finite and Infinite Sets 37 Eger Hungary (1984)391\u2013402.","DOI":"10.1016\/B978-0-444-86893-0.50031-0"},{"key":"e_1_2_1_15_2","first-page":"1","article-title":"A survey of the cycle double cover conjecture","volume":"27","author":"Jaeger F.","year":"1985","journal-title":"Ann. Discrete Math."},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(74)90087-2"},{"key":"e_1_2_1_17_2","unstructured":"H. J.Lai personal communication."},{"key":"e_1_2_1_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-5060(08)70504-1"},{"key":"e_1_2_1_19_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190020207"},{"key":"e_1_2_1_20_2","unstructured":"M.Preissmann Sur les colorations des ar\u011btes des graph cubiques. These de Doctorat de 3\u00e8me cycle Universit\u00e9 de Grenoble (1981)."},{"key":"e_1_2_1_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(80)90158-2"},{"key":"e_1_2_1_22_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972700042660"},{"key":"e_1_2_1_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(86)90054-7"},{"key":"e_1_2_1_24_2","first-page":"553","volume-title":"Proceedings of the Chapel Hill Conference","author":"Tutte W.","year":"1969"},{"key":"e_1_2_1_25_2","first-page":"88","article-title":"Hamiltonian connectedness of line graphs","volume":"22","author":"Zhan S.\u2010M.","year":"1986","journal-title":"Ars Combinat."}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190130408","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190130408","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T14:04:08Z","timestamp":1697983448000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190130408"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,9]]},"references-count":24,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1989,9]]}},"alternative-id":["10.1002\/jgt.3190130408"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190130408","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,9]]}}}