{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:54Z","timestamp":1753893834450,"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>We prove the following best possible result. Let $k\\ge 2$ be an integer and $G$ be a graph of order $n$ with minimum degree at least $k$. Assume $n \\ge 8k-16$ for even $n$ and $n \\ge 6k-13$ for odd $n$. If the degree sum of each pair of nonadjacent vertices of $G$ is at least $n$, then for any given Hamiltonian cycle $C$ of $G$, $G$ has a $[k,\\,k+1]$-factor containing $C$.<\/jats:p>","DOI":"10.37236\/1436","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:01:43Z","timestamp":1578708103000},"source":"Crossref","is-referenced-by-count":1,"title":["A $[k,k+1]$-Factor Containing A Given Hamiltonian Cycle"],"prefix":"10.37236","volume":"6","author":[{"given":"Cai","family":"Mao-cheng","sequence":"first","affiliation":[]},{"given":"Yanjun","family":"Li","sequence":"additional","affiliation":[]},{"given":"Mikio","family":"Kano","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1998,11,27]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v6i1r4\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v6i1r4\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T06:08:18Z","timestamp":1579327698000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v6i1r4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,11,27]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1999,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1436","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1998,11,27]]},"article-number":"R4"}}