{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T21:40:21Z","timestamp":1771623621893,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The main problem considered in this paper is maximizing the number of cycles in a graph with given number of edges. In 2009,\u00a0Kir\u00e1ly conjectured that there is constant $c$ such that any graph with $m$ edges has at most $c(1.4)^m$ cycles. In this paper, it is shown that for sufficiently large $m$, a graph with $m$ edges has at most $(1.443)^m$ cycles. For sufficiently large $m$, examples of a graph with $m$ edges and $(1.37)^m$ cycles are presented. For a graph with given number of vertices and edges an upper bound on the maximal number of cycles is given. Also, bounds tight up to a constant are presented for the maximum number of cycles in a multigraph with given number of edges, as well as in a multigraph with given number of vertices and edges.<\/jats:p>","DOI":"10.37236\/8747","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T06:01:45Z","timestamp":1578636105000},"source":"Crossref","is-referenced-by-count":2,"title":["The Maximum Number of Cycles in a Graph with Fixed Number of Edges"],"prefix":"10.37236","volume":"26","author":[{"given":"Andrii","family":"Arman","sequence":"first","affiliation":[]},{"given":"Sergei","family":"Tsaturian","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,12,6]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i4p42\/7967","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i4p42\/7967","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:01:04Z","timestamp":1579233664000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i4p42"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,6]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2019,10,11]]}},"URL":"https:\/\/doi.org\/10.37236\/8747","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,12,6]]},"article-number":"P4.42"}}