{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,5]],"date-time":"2024-04-05T07:47:09Z","timestamp":1712303229939},"reference-count":13,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2008,8,27]],"date-time":"2008-08-27T00:00:00Z","timestamp":1219795200000},"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":[[2009,2]]},"abstract":"Abstract<\/jats:title>In 1968, Vizing [Uaspekhi Mat Nauk 23 (1968) 117\u2013134; Russian Math Surveys 23 (1968), 125\u2013142] conjectured that for any edge chromatic critical graph ${{G}} = ({{V}}, {{E}})$<\/jats:styled-content> with maximum degree $\\Delta$<\/jats:styled-content>, $|{{E}}| \\geq {{{1}}\\over {{2}}}\\{(\\Delta {{- 1}})|{{V}}| + {{3}}\\}$<\/jats:styled-content>. This conjecture has been verified for $\\Delta \\leq {{5}}$<\/jats:styled-content>. In this article, by applying the discharging method, we prove the conjecture for $\\Delta = {{6}}$<\/jats:styled-content>. \u00a9 2008 Wiley Periodicals, Inc. J Graph Theory 60: 149\u2013171, 2009<\/jats:p>","DOI":"10.1002\/jgt.20351","type":"journal-article","created":{"date-parts":[[2008,8,27]],"date-time":"2008-08-27T18:33:15Z","timestamp":1219861995000},"page":"149-171","source":"Crossref","is-referenced-by-count":22,"title":["The size of edge chromatic critical graphs with maximum degree 6"],"prefix":"10.1002","volume":"60","author":[{"given":"Rong","family":"Luo","sequence":"first","affiliation":[]},{"given":"Lianying","family":"Miao","sequence":"additional","affiliation":[]},{"given":"Yue","family":"Zhao","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2008,8,27]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(76)90139-4"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2005.06.010"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(96)00105-7"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1006\/eujc.1998.0254"},{"key":"e_1_2_1_6_2","first-page":"39","article-title":"Snarks and k\u2010snarks","volume":"25","author":"Chetwynd A. G.","year":"1988","journal-title":"Ars Combin"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(83)90069-9"},{"key":"e_1_2_1_8_2","volume-title":"Edge colorings of graphs","author":"Fiorini S.","year":"1977"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(74)90009-0"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02986658"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.2001.2047"},{"key":"e_1_2_1_12_2","first-page":"9","article-title":"Critical graphs with a given chromatic class (Russian)","volume":"5","author":"Vizing V. G.","year":"1965","journal-title":"Diskret Analiz"},{"key":"e_1_2_1_13_2","first-page":"117","article-title":"Some unsolved problems in graph theory","volume":"23","author":"Vizing V. G.","year":"1968","journal-title":"Uaspekhi Mat Nauk"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/s003730070009"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.20351","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.20351","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T19:48:49Z","timestamp":1697658529000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.20351"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,8,27]]},"references-count":13,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2009,2]]}},"alternative-id":["10.1002\/jgt.20351"],"URL":"https:\/\/doi.org\/10.1002\/jgt.20351","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,8,27]]}}}