{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:00Z","timestamp":1753893840187,"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>Given a one-factorization $\\mathcal{F}$ of the complete bipartite graph $K_{n,n}$,\u00a0let ${\\sf pf}(\\mathcal{F})$ denote the number of Hamiltonian cycles obtained by taking pairwise unions of perfect matchings in $\\mathcal{F}$. Let ${\\sf pf}(n)$ be the maximum of ${\\sf pf}(\\mathcal{F})$ over all one-factorizations $\\mathcal{F}$ of $K_{n,n}$.\u00a0In this work we prove that ${\\sf pf}(n)\\geq n^2\/4$, for all $n\\geq 2$.<\/jats:p>","DOI":"10.37236\/4122","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:29:31Z","timestamp":1578702571000},"source":"Crossref","is-referenced-by-count":1,"title":["A Quantitative Approach to Perfect One-Factorizations of Complete Bipartite Graphs"],"prefix":"10.37236","volume":"22","author":[{"given":"Natacha","family":"Astromujoff","sequence":"first","affiliation":[]},{"given":"Martin","family":"Matamala","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,3,23]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p72\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p72\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:23:40Z","timestamp":1579256620000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i1p72"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,23]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2015,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/4122","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,3,23]]},"article-number":"P1.72"}}