{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,3]],"date-time":"2025-10-03T15:11:50Z","timestamp":1759504310399,"version":"build-2065373602"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We prove that $\\chi(G) \\le \\lceil (\\Delta+1)\/2\\rceil+1$ for any triangle-free graph $G$ of maximum degree $\\Delta$ provided $\\Delta \\ge 524$. This gives tangible progress towards an old problem of Vizing, in a form cast by Reed. We use a method of Hurley and Pirot, which in turn relies on a new counting argument of the second author.<\/jats:p>","DOI":"10.37236\/12703","type":"journal-article","created":{"date-parts":[[2025,10,3]],"date-time":"2025-10-03T14:40:55Z","timestamp":1759502455000},"source":"Crossref","is-referenced-by-count":0,"title":["On Vizing\u2019s Problem for Triangle-Free Graphs"],"prefix":"10.37236","volume":"32","author":[{"given":"Ross J.","family":"Kang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matthieu","family":"Rosenfeld","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2025,10,3]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i4p3\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i4p3\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,3]],"date-time":"2025-10-03T14:40:55Z","timestamp":1759502455000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v32i4p3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,3]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,10,3]]}},"URL":"https:\/\/doi.org\/10.37236\/12703","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,3]]},"article-number":"P4.3"}}