{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T21:18:48Z","timestamp":1648934328786},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2008,9,12]],"date-time":"2008-09-12T00:00:00Z","timestamp":1221177600000},"content-version":"unspecified","delay-in-days":4578,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[1996,3]]},"abstract":"<jats:p>Let <jats:italic>P<\/jats:italic><jats:sub>10<\/jats:sub>\\<jats:italic>e<\/jats:italic> be the graph obtained by deleting an edge from the Petersen graph. We give a decomposition theorem for cubic graphs with no minor isomorphic to <jats:italic>P<\/jats:italic><jats:sub>10<\/jats:sub>\\<jats:italic>e<\/jats:italic>. The decomposition is used to show that graphs in this class are 3-edge-colourable. We also consider an application to a conjecture due to Gr\u00f6tzsch which states that a planar graph is 3-edge-colourable if and only if it is fractionally 3-edge-colourable.<\/jats:p>","DOI":"10.1017\/s0963548300001838","type":"journal-article","created":{"date-parts":[[2008,9,12]],"date-time":"2008-09-12T11:14:35Z","timestamp":1221218075000},"page":"57-78","source":"Crossref","is-referenced-by-count":1,"title":["Excluding Minors in Cubic Graphs"],"prefix":"10.1017","volume":"5","author":[{"given":"K.","family":"Kilakos","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"B.","family":"Shepherd","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2008,9,12]]},"reference":[{"key":"S0963548300001838_ref007","article-title":"Cones, lattices and Hilbert bases of circuits and perfect matchings","author":"Goddyn","year":"1996","journal-title":"Contemporary Mathematics"},{"key":"S0963548300001838_ref001","unstructured":"[1] Alspach B. , Goddyn L. A. and Zhang C. Q. (1996) Graphs with the circuit cover property. Submitted."},{"key":"S0963548300001838_ref010","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(87)90021-9"},{"key":"S0963548300001838_ref013","first-page":"729","article-title":"Remarks on the colouring of maps","volume":"10","author":"Tait","year":"1880","journal-title":"Proc. Royal Soc."},{"key":"S0963548300001838_ref012","doi-asserted-by":"publisher","DOI":"10.1016\/S0095-8956(81)80013-5"},{"key":"S0963548300001838_ref011","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-38.3.423"},{"key":"S0963548300001838_ref014","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9800(66)80004-2"},{"key":"S0963548300001838_ref008","doi-asserted-by":"publisher","DOI":"10.1137\/0210055"},{"key":"S0963548300001838_ref006","first-page":"289","article-title":"Graphes 4-essentiels","volume":"287","author":"Fontet","year":"1978","journal-title":"C.R. Acad. Sci."},{"key":"S0963548300001838_ref015","doi-asserted-by":"publisher","DOI":"10.1007\/BF01594196"},{"key":"S0963548300001838_ref009","first-page":"698","article-title":"On 3-connected graphs without essential 3-cuts or triangles","volume":"33","author":"Kelmans","year":"1986","journal-title":"Soviet Math. Dokl."},{"key":"S0963548300001838_ref016","first-page":"199","volume-title":"Lecture Notes in Mathematics 748","author":"Wormald","year":"1979"},{"key":"S0963548300001838_ref005","first-page":"33","article-title":"Petersen subdivisions in some regular graphs","volume":"44","author":"Ellingham","year":"1984","journal-title":"Congressus Numerantium"},{"key":"S0963548300001838_ref002","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1215\/ijm\/1256049011","article-title":"Every planar map is four-colourable, part I: discharging","volume":"21","author":"Appel","year":"1977","journal-title":"Illinois J. Math."},{"key":"S0963548300001838_ref003","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1215\/ijm\/1256049012","article-title":"Every planar map is four-colourable, part II: reducibility","volume":"21","author":"Appel","year":"1977","journal-title":"Illinois J. Math."},{"key":"S0963548300001838_ref004","first-page":"125","article-title":"Maximum matching and a polyhedron with (0,1) vertices","volume":"69B","author":"Edmonds","year":"1965","journal-title":"J. Res. Nat. Bur."}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548300001838","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,12]],"date-time":"2019-05-12T22:10:55Z","timestamp":1557699055000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548300001838\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,3]]},"references-count":16,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1996,3]]}},"alternative-id":["S0963548300001838"],"URL":"https:\/\/doi.org\/10.1017\/s0963548300001838","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,3]]}}}