{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:21Z","timestamp":1753893861291,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A conjecture by Aharoni and Berger states that every family of $n$ matchings of size $n+1$ in a bipartite multigraph contains a rainbow matching of size $n$. In this paper we prove that matching sizes of $\\left(\\frac 3 2 + o(1)\\right) n$ suffice to guarantee such a rainbow matching, which is asymptotically the same bound as the best known one in case we only aim to find a rainbow matching of size $n-1$. This improves previous results by Aharoni, Charbit and Howard, and Kotlar and Ziv. <\/jats:p>","DOI":"10.37236\/5080","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:25:36Z","timestamp":1578691536000},"source":"Crossref","is-referenced-by-count":7,"title":["An Improved Bound on the Sizes of Matchings Guaranteeing a Rainbow Matching"],"prefix":"10.37236","volume":"23","author":[{"given":"Dennis","family":"Clemens","sequence":"first","affiliation":[]},{"given":"Julia","family":"Ehrenm\u00fcller","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,4,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i2p11\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i2p11\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:30:18Z","timestamp":1579239018000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i2p11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,4,15]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2016,3,31]]}},"URL":"https:\/\/doi.org\/10.37236\/5080","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,4,15]]},"article-number":"P2.11"}}