{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:23Z","timestamp":1753893863857,"version":"3.41.2"},"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>In 1971, Tomescu conjectured [Le nombre des graphes connexes $k$-chromatiques minimaux aux sommets \u00e9tiquet\u00e9s, C. R. Acad. Sci. Paris 273 (1971), 1124--1126] that every connected graph $G$ on $n$ vertices with $\\chi(G) = k \\geq 4$ has at most $k!(k-1)^{n-k}$ $k$-colourings, where equality holds if and only if the graph is formed from $K_k$ by repeatedly adding leaves. In this note we prove (a strengthening of) the conjecture of Tomescu when $k=5$.\r\n<\/jats:p>","DOI":"10.37236\/7879","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T01:45:47Z","timestamp":1578620747000},"source":"Crossref","is-referenced-by-count":1,"title":["Maximum Number of Colourings: 5-Chromatic Case"],"prefix":"10.37236","volume":"26","author":[{"given":"Fiachra","family":"Knox","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bojan","family":"Mohar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2019,8,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i3p40\/7899","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i3p40\/7899","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:09:27Z","timestamp":1579216167000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i3p40"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,30]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,7,4]]}},"URL":"https:\/\/doi.org\/10.37236\/7879","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,8,30]]},"article-number":"P3.40"}}