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We investigate the complexity of whether there exists a sequence of switches that transforms a given \u2010edge\u2010coloured graph  so that it has an edge\u2010colour\u2010preserving homomorphism to a fixed \u2010edge\u2010coloured graph  and give a dichotomy theorem in the case that  acts transitively.<\/jats:p>","DOI":"10.1002\/jgt.23265","type":"journal-article","created":{"date-parts":[[2025,6,3]],"date-time":"2025-06-03T03:00:26Z","timestamp":1748919626000},"page":"200-208","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Dichotomy Theorem for \u0393\u2010Switchable H\u2010Colouring on m\u2010Edge\u2010Coloured Graphs"],"prefix":"10.1002","volume":"110","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7237-4288","authenticated-orcid":false,"given":"Richard","family":"Brewster","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics Thompson Rivers University Kamloops British Columbia Canada"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-4046-2061","authenticated-orcid":false,"given":"Arnott","family":"Kidner","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Mathematik Universit\u00e4t Paderborn Paderborn Deutschland"}]},{"given":"Gary","family":"MacGillivray","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics University of Victoria Victoria British Columbia Canada"}]}],"member":"311","published-online":{"date-parts":[[2025,6,3]]},"reference":[{"volume-title":"Graphs and Homomorphisms","year":"2008","author":"Hell P.","key":"e_1_2_7_2_1"},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.2000.1977"},{"key":"e_1_2_7_4_1","unstructured":"J. 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