{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:04Z","timestamp":1753893844211,"version":"3.41.2"},"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>Let $k&gt;1$, and let $\\mathcal{F}$ be a\u00a0family of\u00a0$2n+k-3$ non-empty sets of edges in a bipartite graph. If the union of every $k$ members of $\\mathcal{F}$\u00a0contains a matching of size $n$, then there exists an $\\mathcal{F}$-rainbow matching of size $n$. Replacing $2n+k-3$ by $2n+k-2$, the result is true also for $k=1$, and it can be proved (for all $k$) both topologically and by a relatively simple combinatorial argument. The main effort is in gaining the last $1$, which makes the result sharp.\u00a0<\/jats:p>","DOI":"10.37236\/9448","type":"journal-article","created":{"date-parts":[[2022,2,2]],"date-time":"2022-02-02T03:12:09Z","timestamp":1643771529000},"source":"Crossref","is-referenced-by-count":2,"title":["Cooperative Conditions for the Existence of Rainbow Matchings"],"prefix":"10.37236","volume":"29","author":[{"given":"Ron","family":"Aharoni","sequence":"first","affiliation":[]},{"given":"Joseph","family":"Briggs","sequence":"additional","affiliation":[]},{"given":"Minho","family":"Cho","sequence":"additional","affiliation":[]},{"given":"Jinha","family":"Kim","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2022,1,28]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i1p23\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i1p23\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,2,2]],"date-time":"2022-02-02T03:13:15Z","timestamp":1643771595000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v29i1p23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,28]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2022,1,27]]}},"URL":"https:\/\/doi.org\/10.37236\/9448","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2022,1,28]]},"article-number":"P1.23"}}