{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:45Z","timestamp":1753893825026,"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>A conjecture of the first two authors is that \u00a0 $n$ matchings of size $n$\u00a0in any graph have a rainbow matching of size $n-1$.\u00a0 We prove a lower bound of $\\frac{2}{3}n-1$, improving on the trivial $\\frac{1}{2}n$, and an analogous result for hypergraphs.\u00a0For\u00a0$\\{C_3,C_5\\}$-free graphs and for disjoint matchings we obtain a lower bound of $\\frac{3n}{4}-O(1)$. We also discuss a conjecture on rainbow alternating paths, that if true would yield a lower bound of $n-\\sqrt{2n}$. We prove the non-alternating (ordinary paths) version of this conjecture.\u00a0<\/jats:p>","DOI":"10.37236\/10173","type":"journal-article","created":{"date-parts":[[2022,2,2]],"date-time":"2022-02-02T03:11:26Z","timestamp":1643771486000},"source":"Crossref","is-referenced-by-count":2,"title":["Rainbow Paths and Large Rainbow Matchings"],"prefix":"10.37236","volume":"29","author":[{"given":"Ron","family":"Aharoni","sequence":"first","affiliation":[]},{"given":"Eli","family":"Berger","sequence":"additional","affiliation":[]},{"given":"Maria","family":"Chudnovsky","sequence":"additional","affiliation":[]},{"given":"Shira","family":"Zerbib","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\/v29i1p10\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i1p10\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,2,2]],"date-time":"2022-02-02T03:12:38Z","timestamp":1643771558000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v29i1p10"}},"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\/10173","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2022,1,28]]},"article-number":"P1.10"}}