{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:42:01Z","timestamp":1753890121329,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","issue":"Graph Theory","license":[{"start":{"date-parts":[[2018,2,1]],"date-time":"2018-02-01T00:00:00Z","timestamp":1517443200000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/4.0"},{"start":{"date-parts":[[2018,2,1]],"date-time":"2018-02-01T00:00:00Z","timestamp":1517443200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/4.0"},{"start":{"date-parts":[[2018,2,1]],"date-time":"2018-02-01T00:00:00Z","timestamp":1517443200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/4.0"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>We examine $t$-colourings of oriented graphs in which, for a fixed integer $k \\geq 1$, vertices joined by a directed path of length at most $k$ must be assigned different colours. A homomorphism model that extends the ideas of Sherk for the case $k=2$ is described. Dichotomy theorems for the complexity of the problem of deciding, for fixed $k$ and $t$, whether there exists such a $t$-colouring are proved.<\/jats:p><jats:p>Comment: 14 pages<\/jats:p>","DOI":"10.23638\/dmtcs-20-1-6","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T16:40:16Z","timestamp":1743698416000},"source":"Crossref","is-referenced-by-count":0,"title":["A Study of $k$-dipath Colourings of Oriented Graphs"],"prefix":"10.23638","volume":"Vol. 20 no. 1","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1657-3172","authenticated-orcid":false,"given":"Christopher","family":"Duffy","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gary","family":"MacGillivray","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"\u00c9ric","family":"Sopena","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2018,2,1]]},"container-title":["Discrete Mathematics &amp; Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1605.08905v4","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1605.08905v4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T16:40:17Z","timestamp":1743698417000},"score":1,"resource":{"primary":{"URL":"http:\/\/dmtcs.episciences.org\/1520"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2,1]]},"references-count":0,"journal-issue":{"issue":"Graph Theory","published-online":{"date-parts":[[2018,2,1]]}},"URL":"https:\/\/doi.org\/10.23638\/dmtcs-20-1-6","relation":{"has-preprint":[{"id-type":"arxiv","id":"1605.08905v3","asserted-by":"subject"},{"id-type":"arxiv","id":"1605.08905v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1605.08905","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1605.08905","asserted-by":"subject"}]},"ISSN":["1365-8050"],"issn-type":[{"type":"electronic","value":"1365-8050"}],"subject":[],"published":{"date-parts":[[2018,2,1]]},"article-number":"1520"}}