{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:17:05Z","timestamp":1758824225535,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A vertex colouring of a graph is nonrepetitive\u00a0if there is no\u00a0path for which the first half of the path is assigned the same\u00a0sequence of colours as the second half. The nonrepetitive\u00a0chromatic number\u00a0of a graph $G$ is the minimum integer $k$ such\u00a0that $G$ has a nonrepetitive $k$-colouring. Whether planar graphs\u00a0have bounded nonrepetitive chromatic number is one of the most\u00a0important open problems in the field. Despite this, the best known\u00a0upper bound is $O(\\sqrt{n})$ for $n$-vertex planar graphs. We prove\u00a0a $O(\\log n)$ upper bound.<\/jats:p>","DOI":"10.37236\/3153","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:58:14Z","timestamp":1578693494000},"source":"Crossref","is-referenced-by-count":7,"title":["Nonrepetitive Colourings of Planar Graphs with $O(\\log  n)$ Colours"],"prefix":"10.37236","volume":"20","author":[{"given":"Vida","family":"Dujmovi\u0107","sequence":"first","affiliation":[]},{"given":"Gwena\u00ebl","family":"Joret","sequence":"additional","affiliation":[]},{"given":"Fabrizio","family":"Frati","sequence":"additional","affiliation":[]},{"given":"David R.","family":"Wood","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,3,1]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p51\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p51\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T06:25:38Z","timestamp":1579242338000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i1p51"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,3,1]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2013,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/3153","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,3,1]]},"article-number":"P51"}}