{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T11:31:21Z","timestamp":1767007881618,"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>We study the following two problems: i) Given a random graph $G_{n, m}$ (a graph drawn uniformly at random from all graphs on $n$ vertices with exactly $m$ edges), can we color its edges with $r$ colors such that no color class contains a component of size $\\Theta(n)$? ii) Given a random graph $G_{n,m}$ with a random partition of its edge set into sets of size $r$, can we color its edges with $r$ colors subject to the restriction that every color is used for exactly one edge in every set of the partition such that no color class contains a component of size $\\Theta(n)$? We prove that for any fixed $r\\geq 2$, in both settings the (sharp) threshold for the existence of such a coloring coincides with the known threshold for $r$-orientability of $G_{n,m}$, which is at $m=rc_r^*n$ for some analytically computable constant $c_r^*$. The fact that the two problems have the same threshold is in contrast with known results for the two corresponding Achlioptas-type problems.<\/jats:p>","DOI":"10.37236\/405","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:00:38Z","timestamp":1578715238000},"source":"Crossref","is-referenced-by-count":5,"title":["Coloring the Edges of a Random Graph without a Monochromatic Giant Component"],"prefix":"10.37236","volume":"17","author":[{"given":"Reto","family":"Sp\u00f6hel","sequence":"first","affiliation":[]},{"given":"Angelika","family":"Steger","sequence":"additional","affiliation":[]},{"given":"Henning","family":"Thomas","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,10,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r133\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r133\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:23:08Z","timestamp":1579303388000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r133"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,10,5]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/405","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2010,10,5]]},"article-number":"R133"}}