{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,17]],"date-time":"2023-09-17T17:11:24Z","timestamp":1694970684598},"reference-count":15,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2016,1,13]],"date-time":"2016-01-13T00:00:00Z","timestamp":1452643200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["STE 792\/2\u20101"],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[2017,2]]},"abstract":"Abstract<\/jats:title>Let G<\/jats:italic> be a bridgeless cubic graph. Consider a list of k<\/jats:italic> 1\u2010factors of G<\/jats:italic>. Let be the set of edges contained in precisely i<\/jats:italic> members of the k<\/jats:italic> 1\u2010factors. Let be the smallest over all lists of k<\/jats:italic> 1\u2010factors of G<\/jats:italic>. We study lists by three 1\u2010factors, and call with a \u2010core of G<\/jats:italic>. If G<\/jats:italic> is not 3\u2010edge\u2010colorable, then . In Steffen (J\u00a0Graph Theory 78 (2015), 195\u2013206) it is shown that if , then is an upper bound for the girth of G<\/jats:italic>. We show that bounds the oddness of G<\/jats:italic> as well. We prove that . If , then every \u2010core has a very specific structure. We call these cores Petersen cores. We show that for any given oddness there is a cyclically 4\u2010edge\u2010connected cubic graph G<\/jats:italic> with . On the other hand, the difference between and can be arbitrarily big. This is true even if we additionally fix the oddness. Furthermore, for every integer , there exists a bridgeless cubic graph G<\/jats:italic> such that .<\/jats:p>","DOI":"10.1002\/jgt.22014","type":"journal-article","created":{"date-parts":[[2016,1,14]],"date-time":"2016-01-14T03:35:14Z","timestamp":1452742514000},"page":"109-120","source":"Crossref","is-referenced-by-count":4,"title":["Petersen Cores and the Oddness of Cubic Graphs"],"prefix":"10.1002","volume":"84","author":[{"given":"Ligang","family":"Jin","sequence":"first","affiliation":[{"name":"PADERBORN INSTITUTE FOR ADVANCED STUDIES IN COMPUTER SCIENCE AND ENGINEERING AND INSTITUTE FOR MATHEMATICS PADERBORN UNIVERSITY WARBURGER STREET 100 33102 PADERBORN GERMANY"}]},{"given":"Eckhard","family":"Steffen","sequence":"additional","affiliation":[{"name":"PADERBORN INSTITUTE FOR ADVANCED STUDIES IN COMPUTER SCIENCE AND ENGINEERING AND INSTITUTE FOR MATHEMATICS PADERBORN UNIVERSITY WARBURGER STREET 100 33102 PADERBORN GERMANY"}]}],"member":"311","published-online":{"date-parts":[[2016,1,13]]},"reference":[{"key":"e_1_2_4_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190110104"},{"key":"e_1_2_4_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.21778"},{"key":"e_1_2_4_4_1","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.1994.1039"},{"key":"e_1_2_4_5_1","doi-asserted-by":"publisher","DOI":"10.1038\/scientificamerican0476-126"},{"key":"e_1_2_4_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(81)90030-7"},{"key":"e_1_2_4_7_1","doi-asserted-by":"crossref","unstructured":"J.H\u00e4gglund On snarks that are far from being 3\u2010edge\u2010colorable arXiv: 1203.2015v1 (2012).","DOI":"10.37236\/3430"},{"key":"e_1_2_4_8_1","doi-asserted-by":"publisher","DOI":"10.2307\/2319844"},{"issue":"1","key":"e_1_2_4_9_1","first-page":"51","article-title":"Small snarks with large oddness","volume":"22","author":"Lukot'ka R.","year":"2015","journal-title":"Electron J Comb"},{"key":"e_1_2_4_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-014-2550-4"},{"key":"e_1_2_4_11_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0118(199607)22:3<253::AID-JGT6>3.0.CO;2-L"},{"key":"e_1_2_4_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02392606"},{"key":"e_1_2_4_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(97)00255-0"},{"key":"e_1_2_4_14_1","doi-asserted-by":"crossref","unstructured":"E.Steffen Intersecting 1\u2010factors and nowhere\u2010zero 5\u2010flows Combinatorica35(2015) 633\u2013640.","DOI":"10.1007\/s00493-014-3034-2"},{"key":"e_1_2_4_15_1","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.21798"},{"key":"e_1_2_4_16_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579225"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.22014","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.22014","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.22014","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,17]],"date-time":"2023-09-17T16:51:25Z","timestamp":1694969485000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.22014"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1,13]]},"references-count":15,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2017,2]]}},"alternative-id":["10.1002\/jgt.22014"],"URL":"http:\/\/dx.doi.org\/10.1002\/jgt.22014","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,1,13]]}}}
