{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:47Z","timestamp":1753893827511,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Given a graph $G$ with only even degrees, let $\\varepsilon(G)$ denote the number of Eulerian orientations, and let $h(G)$ denote the number of half graphs, that is, subgraphs $F$ such that $d_F(v)=d_G(v)\/2$ for each vertex $v$. Recently, Borb\u00e9nyi and Csikv\u00e1ri proved that\u00a0 $\\varepsilon(G)\\geq h(G)$ holds true for all Eulerian graphs, with equality if and only if $G$ is bipartite. In this paper we give a simple new proof of this fact, and we give identities and inequalities for the number of Eulerian orientations and half graphs of a $2$-cover\u00a0of a graph $G$.<\/jats:p>","DOI":"10.37236\/8767","type":"journal-article","created":{"date-parts":[[2020,9,4]],"date-time":"2020-09-04T02:48:26Z","timestamp":1599187706000},"source":"Crossref","is-referenced-by-count":0,"title":["Covers, Orientations and Factors"],"prefix":"10.37236","volume":"27","author":[{"given":"P\u00e9ter","family":"Csikv\u00e1ri","sequence":"first","affiliation":[]},{"given":"Andr\u00e1s","family":"Imolay","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2020,8,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p25\/8143","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p25\/8143","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,4]],"date-time":"2020-09-04T02:48:27Z","timestamp":1599187707000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i3p25"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,7]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,7,9]]}},"URL":"https:\/\/doi.org\/10.37236\/8767","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,8,7]]},"article-number":"P3.25"}}