{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T07:50:59Z","timestamp":1776844259978,"version":"3.51.2"},"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>Algorithms for classifying one-factorizations of regular graphs are studied.  The smallest open case is currently graphs of order 12; one-factorizations of $r$-regular graphs of order 12 are here classified for $r\\leq 6$ and $r=10,11$.  Two different approaches are used for regular graphs of small degree; these proceed one-factor by one-factor and vertex by vertex, respectively. For degree $r=11$, we have one-factorizations of $K_{12}$. These have earlier been classified, but a new approach is presented which views these as certain triple systems on $4n-1$ points and utilizes an approach developed for classifying Steiner triple systems.  Some properties of the classified one-factorizations are also tabulated.  <\/jats:p>","DOI":"10.37236\/1899","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:19:49Z","timestamp":1578719989000},"source":"Crossref","is-referenced-by-count":4,"title":["One-Factorizations of Regular Graphs of Order 12"],"prefix":"10.37236","volume":"12","author":[{"given":"Petteri","family":"Kaski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Patric R. J.","family":"\u00d6sterg\u00e5rd","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"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\/v12i1r2\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r2\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:51:46Z","timestamp":1579323106000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v12i1r2"}},"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\/1899","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,1,7]]},"article-number":"R2"}}