{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,5]],"date-time":"2024-03-05T01:21:10Z","timestamp":1709601670565},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"For every $n\\in\\mathbb{N}$ and $k\\geqslant2$, it is known that every $k$-edge-colouring of the complete graph on $n$ vertices contains a monochromatic connected component of order at least $\\frac{n}{k-1}$. For $k\\geqslant3$, it is known that the complete graph can be replaced by a graph $G$ with $\\delta(G)\\geqslant(1-\\varepsilon_k)n$ for some constant $\\varepsilon_k$. In this paper, we show that the maximum possible value of $\\varepsilon_3$ is $\\frac16$. This disproves a conjecture of Gy\u00e1rfas and S\u00e1rk\u00f6zy.<\/jats:p>","DOI":"10.37236\/9039","type":"journal-article","created":{"date-parts":[[2021,1,14]],"date-time":"2021-01-14T06:13:25Z","timestamp":1610604805000},"source":"Crossref","is-referenced-by-count":2,"title":["Monochromatic Components in Edge-Coloured Graphs with Large Minimum Degree"],"prefix":"10.37236","volume":"28","author":[{"given":"Hannah","family":"Guggiari","sequence":"first","affiliation":[]},{"given":"Alex","family":"Scott","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2021,1,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i1p10\/8250","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i1p10\/8250","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,1,14]],"date-time":"2021-01-14T06:13:25Z","timestamp":1610604805000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v28i1p10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,15]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1,14]]}},"URL":"https:\/\/doi.org\/10.37236\/9039","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,15]]}}}