{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T18:28:59Z","timestamp":1773080939089,"version":"3.50.1"},"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>Using a recent result of Chudnovsky, Seymour, and Sullivan, we slightly improve two bounds related to the Caccetta-Haggkvist Conjecture. Namely, we show that if $\\alpha\\geq 0.35312$, then each $n$-vertex digraph $D$ with minimum outdegree at least $\\alpha n$ has a directed $3$-cycle.  If $\\beta\\geq 0.34564$, then every $n$-vertex digraph $D$ in which the outdegree and the indegree of each vertex is at least $\\beta n$ has a directed $3$-cycle.<\/jats:p>","DOI":"10.37236\/1020","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:48:29Z","timestamp":1578718109000},"source":"Crossref","is-referenced-by-count":13,"title":["On Directed Triangles in Digraphs"],"prefix":"10.37236","volume":"14","author":[{"given":"Peter","family":"Hamburger","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Penny","family":"Haxell","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexandr","family":"Kostochka","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2007,9,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1n19\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1n19\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:01:19Z","timestamp":1579320079000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v14i1n19"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,9,7]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2007,1,3]]}},"URL":"https:\/\/doi.org\/10.37236\/1020","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,9,7]]},"article-number":"N19"}}