{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:03Z","timestamp":1753893843746,"version":"3.41.2"},"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>In this paper, we study the question of finding a set of $k$ vertex-disjoint cycles (resp. directed cycles) of distinct lengths in a given graph (resp. digraph). In the context of undirected graphs, we prove that, for every $k \\geq 1$, every graph with minimum degree at least $\\frac{k^2+5k-2}{2}$ has $k$ vertex-disjoint cycles of different lengths, where the degree bound is best possible. We also consider other cases such as when the graph is triangle-free, or the $k$ cycles are required to have different lengths modulo some value $r$. In the context of directed graphs, we consider a conjecture of Lichiardopol concerning the least minimum out-degree required for a digraph to have $k$ vertex-disjoint directed cycles of different lengths. We verify this conjecture for tournaments, and, by using the probabilistic method, for some regular digraphs and digraphs of small order.<\/jats:p>","DOI":"10.37236\/6921","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:42:48Z","timestamp":1578670968000},"source":"Crossref","is-referenced-by-count":8,"title":["Disjoint Cycles of Different Lengths in Graphs and Digraphs"],"prefix":"10.37236","volume":"24","author":[{"given":"Julien","family":"Bensmail","sequence":"first","affiliation":[]},{"given":"Ararat","family":"Harutyunyan","sequence":"additional","affiliation":[]},{"given":"Ngoc Khang","family":"Le","sequence":"additional","affiliation":[]},{"given":"Binlong","family":"Li","sequence":"additional","affiliation":[]},{"given":"Nicolas","family":"Lichiardopol","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,12,8]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i4p37\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i4p37\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:41:56Z","timestamp":1579236116000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i4p37"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12,8]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2017,10,5]]}},"URL":"https:\/\/doi.org\/10.37236\/6921","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2017,12,8]]},"article-number":"P4.37"}}