{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:43:40Z","timestamp":1759063420904,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Answering a question posed by Caro, Hansberg, Lauri, and Zarb, we show that for every positive integer $n$ and every function $\\sigma\\colon E(K_{4n})\\to\\{-1,1\\}$ with $\\sigma\\left(E(K_{4n})\\right)=0$, there is a perfect matching $M$ in $K_{4n}$with $\\sigma(M)=0$. Strengthening the consequence of a result of Caro and Yuster, we show that for every positive integer $n$ and every function $\\sigma\\colon E(K_{4n})\\to\\{-1,1\\}$ with $\\left|\\sigma\\left(E(K_{4n})\\right)\\right|&lt;n^2+11n+2,$ there is a perfect matching $M$ in $K_{4n}$ with $|\\sigma(M)|\\leq 2$. Both these results are best possible.<\/jats:p>","DOI":"10.37236\/9994","type":"journal-article","created":{"date-parts":[[2020,12,24]],"date-time":"2020-12-24T01:44:20Z","timestamp":1608774260000},"source":"Crossref","is-referenced-by-count":2,"title":["Low Weight Perfect Matchings"],"prefix":"10.37236","volume":"27","author":[{"given":"Stefan","family":"Ehard","sequence":"first","affiliation":[]},{"given":"Elena","family":"Mohr","sequence":"additional","affiliation":[]},{"given":"Dieter","family":"Rautenbach","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2020,12,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i4p49\/8230","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i4p49\/8230","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,24]],"date-time":"2020-12-24T01:44:21Z","timestamp":1608774261000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i4p49"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,24]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,10,2]]}},"URL":"https:\/\/doi.org\/10.37236\/9994","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,12,24]]},"article-number":"P4.49"}}