{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:43:33Z","timestamp":1759063413476,"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 describe an algorithm which enumerates all Hamilton cycles of a given 3-regular $n$-vertex graph in time $O(1.276^{n})$, improving on Eppstein's previous bound. The resulting new upper bound of $O(1.276^{n})$ for the maximum number of Hamilton cycles in 3-regular $n$-vertex graphs gets close to the best known lower bound of $\\Omega(1.259^{n})$. Our method differs from Eppstein's in that he considers in each step a new graph and modifies it, while we fix (at the very beginning) one Hamilton cycle $C$ and then proceed around $C$, successively producing partial Hamilton cycles.<\/jats:p>","DOI":"10.37236\/619","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:46:35Z","timestamp":1578714395000},"source":"Crossref","is-referenced-by-count":3,"title":["Enumerating all Hamilton Cycles and Bounding the Number of Hamilton Cycles in 3-Regular Graphs"],"prefix":"10.37236","volume":"18","author":[{"given":"Heidi","family":"Gebauer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,6,21]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p132\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p132\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:08:48Z","timestamp":1579302528000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p132"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,6,21]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/619","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,6,21]]},"article-number":"P132"}}