{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,23]],"date-time":"2026-07-23T22:37:31Z","timestamp":1784846251592,"version":"3.55.0"},"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>An $r$-edge-coloring of a graph is an assignment of $r$ colors to the edges of the graph.  An exactly $r$-edge-coloring of a graph is an $r$-edge-coloring of the graph that uses all $r$ colors. A matching of an edge-colored graph is called rainbow matching, if no two edges have the same color in the matching.  In this paper, we prove that an exactly $r$-edge-colored complete graph of order $n$ has a rainbow matching of size $k(\\ge 2)$ if $r \\ge max\\{{2k-3\\choose 2}+2, {k-2\\choose 2}+(k-2)(n-k+2)+2 \\}$, $k \\ge 2$, and $n \\ge 2k+1$. The bound on $r$ is best possible.<\/jats:p>","DOI":"10.37236\/140","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:32:11Z","timestamp":1578717131000},"source":"Crossref","is-referenced-by-count":26,"title":["A Rainbow $k$-Matching in the Complete Graph with $r$ Colors"],"prefix":"10.37236","volume":"16","author":[{"given":"Shinya","family":"Fujita","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Atsushi","family":"Kaneko","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ingo","family":"Schiermeyer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kazuhiro","family":"Suzuki","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2009,4,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r51\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r51\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T02:55:56Z","timestamp":1579316156000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r51"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,4,30]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/140","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,4,30]]},"article-number":"R51"}}