{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:43:42Z","timestamp":1759063422348,"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 $1$-factorisation of a graph $G$ is a decomposition of $G$ into edge-disjoint $1$-factors (perfect matchings), and a perfect $1$-factorisation is a $1$-factorisation in which the union of any two of the $1$-factors is a Hamilton cycle.\u00a0 We consider the problem of the existence of perfect $1$-factorisations of even order circulant graphs with small degree.\u00a0 In particular, we characterise the $3$-regular circulant graphs that admit a perfect $1$-factorisation and we solve the existence problem for a large family of $4$-regular circulants.\u00a0 Results of computer searches for perfect\u00a0 $1$-factorisations of $4$-regular circulant graphs of orders up to $30$ are provided and some problems are posed.<\/jats:p>","DOI":"10.37236\/2264","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:57:03Z","timestamp":1578711423000},"source":"Crossref","is-referenced-by-count":4,"title":["Perfect 1-Factorisations of Circulants with Small Degree"],"prefix":"10.37236","volume":"20","author":[{"given":"Sarada","family":"Herke","sequence":"first","affiliation":[]},{"given":"Barbara","family":"Maenhaut","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,3,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p58\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p58\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:25:20Z","timestamp":1579260320000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i1p58"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,3,24]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2013,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/2264","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,3,24]]},"article-number":"P58"}}