{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:46:36Z","timestamp":1759063596477,"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 graph admitting a perfect matching has the Perfect\u2013Matching\u2013Hamiltonian property (for short the PMH\u2013property) if each of its perfect matchings can be extended to a hamiltonian cycle. In this paper we establish some sufficient conditions for a graph $G$ in order to guarantee that its line graph $L(G)$ has the PMH\u2013property. In particular, we prove that this happens when $G$ is (i) a Hamiltonian graph with maximum degree at most 3, (ii) a complete graph, (iii) a balanced complete bipartite graph with at least 100 vertices, or (iv) an arbitrarily traceable graph. Further related questions and open problems are proposed along the paper.<\/jats:p>","DOI":"10.37236\/9143","type":"journal-article","created":{"date-parts":[[2021,1,14]],"date-time":"2021-01-14T06:13:21Z","timestamp":1610604801000},"source":"Crossref","is-referenced-by-count":3,"title":["Extending Perfect Matchings to Hamiltonian Cycles in Line Graphs"],"prefix":"10.37236","volume":"28","author":[{"given":"Mari\u00e9n","family":"Abreu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"John Baptist","family":"Gauci","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Domenico","family":"Labbate","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giuseppe","family":"Mazzuoccolo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jean Paul","family":"Zerafa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2021,1,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i1p7\/8247","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i1p7\/8247","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,1,14]],"date-time":"2021-01-14T06:13:21Z","timestamp":1610604801000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v28i1p7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,15]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1,14]]}},"URL":"https:\/\/doi.org\/10.37236\/9143","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2021,1,15]]},"article-number":"P1.7"}}