{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T08:17:10Z","timestamp":1774513030194,"version":"3.50.1"},"reference-count":18,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2019,3,1]],"date-time":"2019-03-01T00:00:00Z","timestamp":1551398400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2019,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For an edge-coloured graph <jats:italic>G<\/jats:italic>, the minimum colour degree of <jats:italic>G<\/jats:italic> means the minimum number of colours on edges which are incident to each vertex of <jats:italic>G<\/jats:italic>. We prove that if <jats:italic>G<\/jats:italic> is an edge-coloured graph with minimum colour degree at least 5, then <jats:italic>V<\/jats:italic>(<jats:italic>G<\/jats:italic>) can be partitioned into two parts such that each part induces a subgraph with minimum colour degree at least 2. We show this theorem by proving amuch stronger form. Moreover, we point out an important relationship between our theorem and Bermond and Thomassen\u2019s conjecture in digraphs.<\/jats:p>","DOI":"10.1017\/s0963548319000014","type":"journal-article","created":{"date-parts":[[2019,3,1]],"date-time":"2019-03-01T05:43:04Z","timestamp":1551418984000},"page":"755-767","source":"Crossref","is-referenced-by-count":7,"title":["Decomposing edge-coloured graphs under colour degree constraints"],"prefix":"10.1017","volume":"28","author":[{"given":"Shinya","family":"Fujita","sequence":"first","affiliation":[]},{"given":"Ruonan","family":"Li","sequence":"additional","affiliation":[]},{"given":"Guanghui","family":"Wang","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2019,3,1]]},"reference":[{"key":"S0963548319000014_ref12","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.22060"},{"key":"S0963548319000014_ref10","unstructured":"[10] Li, R. , Broersma, H. and Zhang, S. (2017) Vertex-disjoint properly edge-colored cycles in edge-colored complete graphs. arXiv:1708.08641"},{"key":"S0963548319000014_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(83)90008-4"},{"key":"S0963548319000014_ref7","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.22163"},{"key":"S0963548319000014_ref4","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190050102"},{"key":"S0963548319000014_ref13","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190050403"},{"key":"S0963548319000014_ref2","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548306008042"},{"key":"S0963548319000014_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.endm.2017.06.078"},{"key":"S0963548319000014_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579195"},{"key":"S0963548319000014_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2018.04.027"},{"key":"S0963548319000014_ref3","unstructured":"[3] Alon, N. , Bang-Jensen, J. and Bessy, S. (2017) Out-colourings of digraphs. arXiv:1706.06441v3"},{"key":"S0963548319000014_ref11","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0118(199611)23:3<321::AID-JGT12>3.0.CO;2-H"},{"key":"S0963548319000014_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/BF02020961"},{"key":"S0963548319000014_ref18","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.1997.1728"},{"key":"S0963548319000014_ref16","first-page":"402","volume-title":"Combinatorial Mathematics: Proceedings of the Third International Conference","author":"Thomassen","year":"1989"},{"key":"S0963548319000014_ref17","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2018.03.005"},{"key":"S0963548319000014_ref1","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.1996.0062"},{"key":"S0963548319000014_ref15","first-page":"97","volume-title":"Selected Topics in Graph Theory III","author":"Thomassen","year":"1988"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548319000014","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,11]],"date-time":"2019-09-11T03:51:33Z","timestamp":1568173893000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548319000014\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,1]]},"references-count":18,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2019,9]]}},"alternative-id":["S0963548319000014"],"URL":"https:\/\/doi.org\/10.1017\/s0963548319000014","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,3,1]]}}}