{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:09Z","timestamp":1753893789734,"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 $G$ be an Eulerian bipartite digraph with vertex partition sizes $m,n$. We prove the following Tur\u00e1n-type result: If $e(G) &gt; 2mn\/3$ then $G$ contains a directed cycle of length at most 4. The result is sharp. We also show that if $e(G)=2mn\/3$ and no directed cycle of length at most 4 exists, then $G$ must be biregular. We apply this result in order to obtain an improved upper bound for the diameter of interchange graphs.<\/jats:p>","DOI":"10.37236\/1667","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:26:52Z","timestamp":1578709612000},"source":"Crossref","is-referenced-by-count":1,"title":["A Note on the Number of Edges Guaranteeing a $C_4$ in Eulerian Bipartite Digraphs"],"prefix":"10.37236","volume":"9","author":[{"given":"Jian","family":"Shen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Raphael","family":"Yuster","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2002,3,21]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v9i1n6\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v9i1n6\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:15:00Z","timestamp":1579324500000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v9i1n6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,3,21]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2002,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1667","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2002,3,21]]},"article-number":"N6"}}