{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:49Z","timestamp":1753893829962,"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 $\\vec H$ be an orientation of a graph $H$. Alon and Yuster proposed the problem of determining or estimating $D(n,m,\\vec H)$, the maximum number of $\\vec H$-free orientations\u00a0a graph with $n$ vertices and $m$ edges may have. We consider the maximum number of $\\vec H$-free orientations of typical graphs $G(n,m)$ with $n$\u00a0vertices and $m$ edges. Suppose $\\vec H =C^\\circlearrowright_\\ell $ is the directed cycle of length $\\ell\\geq 3$. We show that if ${m\\gg n^{1+1\/(\\ell-1)}}$, then this maximum is $2^{o(m)}$, while if ${m\\ll n^{1+1\/(\\ell-1)}}$, then it is $2^{(1-o(1))m}$.<\/jats:p>","DOI":"10.37236\/3699","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:08:28Z","timestamp":1578704908000},"source":"Crossref","is-referenced-by-count":4,"title":["On the Number of Orientations of Random Graphs with No Directed Cycles of a Given Length"],"prefix":"10.37236","volume":"21","author":[{"given":"P.","family":"Allen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Y.","family":"Kohayakawa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G. O.","family":"Mota","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R. F.","family":"Parente","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2014,3,10]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i1p52\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i1p52\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:02:03Z","timestamp":1579258923000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v21i1p52"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,3,10]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2014,1,13]]}},"URL":"https:\/\/doi.org\/10.37236\/3699","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2014,3,10]]},"article-number":"P1.52"}}