{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,30]],"date-time":"2025-09-30T10:39:49Z","timestamp":1759228789437,"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>In this paper, we consider a weakening of the definitions of uniform and perfect one-factorizations of the complete graph.  Basically, we want to order the $2n-1$ one-factors of a one-factorization of the complete graph $K_{2n}$ in such a way that the union of any two (cyclically) consecutive one-factors is always isomorphic to the same two-regular graph.  This property is termed sequentially uniform; if this two-regular graph is a Hamiltonian cycle, then the property is termed sequentially perfect.  We will discuss several methods for constructing sequentially uniform and sequentially perfect one-factorizations. In particular, we prove for any integer $n \\geq 1$ that there is a sequentially perfect one-factorization of $K_{2n}$.  As well, for any odd integer $m \\geq 1$, we prove that there is a sequentially uniform one-factorization of $K_{2^t m}$ of type $(4,4,\\dots,4)$ for all integers $t \\geq 2 + \\lceil \\log_2 m \\rceil$ (where type $(4,4,\\dots,4)$ denotes a two-regular graph consisting of disjoint cycles of length four).<\/jats:p>","DOI":"10.37236\/1898","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:19:51Z","timestamp":1578719991000},"source":"Crossref","is-referenced-by-count":10,"title":["Sequentially Perfect and Uniform One-Factorizations of the  Complete Graph"],"prefix":"10.37236","volume":"12","author":[{"given":"Jeffrey H.","family":"Dinitz","sequence":"first","affiliation":[]},{"given":"Peter","family":"Dukes","sequence":"additional","affiliation":[]},{"given":"Douglas R.","family":"Stinson","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2005,1,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r1\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r1\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:51:50Z","timestamp":1579323110000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v12i1r1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,1,7]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2005,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1898","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2005,1,7]]},"article-number":"R1"}}