{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:34Z","timestamp":1753893814413,"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 settle Alspach's problem in the case of Hamilton cycles and 5-cycles; that is, we show that for all odd integers $n\\ge 5$ and all nonnegative integers $h$ and $t$ with $hn + 5t = n(n-1)\/2$, the complete graph $K_n$ decomposes into $h$ Hamilton cycles and $t$ 5-cycles and for all even integers $n \\ge 6$ and all nonnegative integers $h$ and $t$ with $hn + 5t = n(n-2)\/2$, the complete graph $K_n$ decomposes into $h$ Hamilton cycles, $t$ 5-cycles, and a $1$-factor.  We also settle Alspach's problem in the case of Hamilton cycles and 4-cycles.<\/jats:p>","DOI":"10.37236\/569","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:51:26Z","timestamp":1578714686000},"source":"Crossref","is-referenced-by-count":0,"title":["Alspach's Problem: The Case of Hamilton Cycles and 5-Cycles"],"prefix":"10.37236","volume":"18","author":[{"given":"Heather","family":"Jordon","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,4,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p82\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p82\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:14:23Z","timestamp":1579302863000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p82"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,4,7]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/569","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,4,7]]},"article-number":"P82"}}