{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:37:30Z","timestamp":1787323050835,"version":"build-2736575974"},"reference-count":21,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12071260"],"award-info":[{"award-number":["12071260"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2023,3,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Let [Formula: see text] be a digraph of order [Formula: see text]. We define the degree of vertex [Formula: see text] in [Formula: see text] to be [Formula: see text], where [Formula: see text] and [Formula: see text] are the out-degree and in-degree of [Formula: see text] in [Formula: see text], respectively. Let [Formula: see text] be a positive integer and let [Formula: see text] be any given subset of [Formula: see text] with [Formula: see text]. In this paper we show that if [Formula: see text] for all [Formula: see text], then for any integer partition [Formula: see text] with [Formula: see text] for each [Formula: see text], there are [Formula: see text] disjoint cycles containing exactly [Formula: see text] vertices of [Formula: see text], respectively. The degree condition [Formula: see text] is sharp in some sense and this result confirms the conjecture posed by Wang [J. Graph Theory, 34 (2000), pp. 154\u2013162] as a corollary. The result in this paper implies a theorem on cycle-factors containing matchings in bipartite graphs. Further, the special case [Formula: see text] is a directed version of the Aigner\u2013Brandt theorem on disjoint cycles in graphs.<\/jats:p>","DOI":"10.1137\/21m1460594","type":"journal-article","created":{"date-parts":[[2023,2,1]],"date-time":"2023-02-01T19:43:41Z","timestamp":1675280621000},"page":"221-232","source":"Crossref","is-referenced-by-count":2,"title":["Disjoint Cycles in a Digraph with Partial Degree"],"prefix":"10.1137","volume":"37","author":[{"given":"Hong","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Mathematics, The University of Idaho, Moscow, ID 83844 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yun","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics, Shandong University, Jinan 250100, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jin","family":"Yan","sequence":"additional","affiliation":[{"name":"Corresponding author. 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