{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T04:40:43Z","timestamp":1776660043971,"version":"3.51.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We propose a new proof technique that applies to the same problems as the\u00a0 Lov\u00e1sz Local Lemma or the entropy-compression method. We present this approach in the context of non-repetitive colorings and we use it to improve upper-bounds relating different non-repetitive chromatic numbers to the maximal degree of a graph. It seems that there should be other interesting applications of the presented approach.\r\nIn terms of upper-bounds our approach seems to be as strong as entropy-compression, but the proofs are more elementary and shorter. The applications we provide in this paper are upper bounds for graphs of maximal degree at most $\\Delta$: a minor improvement on the upper-bound of the non-repetitive chromatic number, a $4.25\\Delta +o(\\Delta)$ upper-bound on the weak total non-repetitive chromatic number, and a $ \\Delta^2+\\frac{3}{2^{1\/3}}\\Delta^{5\/3}+ o(\\Delta^{5\/3})$ upper-bound on the total non-repetitive chromatic number of graphs. This last result implies the same upper-bound for the non-repetitive chromatic index of graphs, which improves the best known bound.\u00a0<\/jats:p>","DOI":"10.37236\/9667","type":"journal-article","created":{"date-parts":[[2020,9,4]],"date-time":"2020-09-04T02:46:54Z","timestamp":1599187614000},"source":"Crossref","is-referenced-by-count":16,"title":["Another Approach to Non-Repetitive Colorings of Graphs of Bounded Degree"],"prefix":"10.37236","volume":"27","author":[{"given":"Matthieu","family":"Rosenfeld","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,9,4]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p43\/8161","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p43\/8161","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,4]],"date-time":"2020-09-04T02:46:54Z","timestamp":1599187614000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i3p43"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,4]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,7,9]]}},"URL":"https:\/\/doi.org\/10.37236\/9667","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9,4]]},"article-number":"P3.43"}}