{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:16Z","timestamp":1753893856095,"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 simple 2-matching in a graph is a subgraph all of whose nodes have degree $1$ or $2$. A simple 2-matching is called $k$-restricted if every connected component has $&gt;k$ edges. We consider the problem of finding a $k$-restricted simple 2-matching with a maximum number of edges, which is a relaxation of the problem of finding a Hamilton cycle in a graph. Our main result is a min-max theorem for the maximum number of edges in a 1-restricted simple 2-matching. We prove this result constructively by presenting a polynomial time algorithm for finding a 1-restricted simple 2-matching with a maximum number of edges.<\/jats:p>","DOI":"10.37236\/991","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:48:00Z","timestamp":1578718080000},"source":"Crossref","is-referenced-by-count":3,"title":["Maximum Cardinality 1-Restricted Simple 2-Matchings"],"prefix":"10.37236","volume":"14","author":[{"given":"David","family":"Hartvigsen","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2007,11,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r73\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r73\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:00:50Z","timestamp":1579320050000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v14i1r73"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,11,5]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2007,1,3]]}},"URL":"https:\/\/doi.org\/10.37236\/991","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2007,11,5]]},"article-number":"R73"}}