{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:12Z","timestamp":1753893852210,"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 consider the question of the existence of homomorphisms between $G_{n,p}$ and odd cycles when $p=c\/n$, $1&lt;c\\leq 4$. We show that for any positive integer $\\ell$, there exists $\\epsilon=\\epsilon(\\ell)$ such that if $c=1+\\epsilon$ then w.h.p. $G_{n,p}$ has a homomorphism from $G_{n,p}$ to $C_{2\\ell+1}$ so long as its odd-girth is at least $2\\ell+1$. On the other hand, we show that if $c=4$ then w.h.p. there is no homomorphism from $G_{n,p}$ to $C_5$. Note that in our range of interest, $\\chi(G_{n,p})=3$ w.h.p., implying that there is a homomorphism from $G_{n,p}$ to $C_3$.\u00a0 These results imply the existence of random graphs with circular chromatic numbers $\\chi_c$ satisfying $2&lt;\\chi_c(G)&lt;2+\\delta$ for arbitrarily small $\\delta$, and also that $2.5\\leq \\chi_c(G_{n,\\frac 4 n})&lt;3$ w.h.p.<\/jats:p>","DOI":"10.37236\/4673","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:31:47Z","timestamp":1578702707000},"source":"Crossref","is-referenced-by-count":1,"title":["Between 2- and 3-Colorability"],"prefix":"10.37236","volume":"22","author":[{"given":"Alan","family":"Frieze","sequence":"first","affiliation":[]},{"given":"Wesley","family":"Pegden","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,2,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p34\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p34\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:37:01Z","timestamp":1579257421000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i1p34"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2,16]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2015,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/4673","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,2,16]]},"article-number":"P1.34"}}