{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:05Z","timestamp":1753893845823,"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>Let $\\Omega_q$ denote the set of proper $[q]$-colorings of the random graph $G_{n,m}, m=dn\/2$ and let $H_q$ be the graph with vertex set $\\Omega_q$ and an edge $\\{\\sigma,\\tau\\}$ where $\\sigma,\\tau$ are mappings $[n]\\to[q]$ iff $h(\\sigma,\\tau)=1$. Here $h(\\sigma,\\tau)$ is the Hamming distance $|\\{v\\in [n]:\\sigma(v)\\neq\\tau(v)\\}|$. We show that w.h.p. $H_q$ contains a single giant component containing almost all colorings in $\\Omega_q$ if $d$ is sufficiently large and $q\\geq \\frac{cd}{\\log d}$ for a constant $c&gt;3\/2$.<\/jats:p>","DOI":"10.37236\/7040","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:35:35Z","timestamp":1578670535000},"source":"Crossref","is-referenced-by-count":1,"title":["Constraining the Clustering Transition for Colorings of Sparse Random Graphs"],"prefix":"10.37236","volume":"25","author":[{"given":"Michael","family":"Anastos","sequence":"first","affiliation":[]},{"given":"Alan","family":"Frieze","sequence":"additional","affiliation":[]},{"given":"Wesley","family":"Pegden","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,3,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p72\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p72\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:35:22Z","timestamp":1579235722000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i1p72"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,29]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,1,12]]}},"URL":"https:\/\/doi.org\/10.37236\/7040","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,3,29]]},"article-number":"P1.72"}}