{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T11:53:27Z","timestamp":1767182007692,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We state a sufficient condition for the square of a locally finite graph to contain a Hamilton circle, extending a result of Harary and Schwenk about finite graphs.\u00a0We also give an alternative proof of an extension to locally finite graphs of the result of Chartrand and Harary that a finite graph not containing $K^4$ or $K_{2,3}$ as a minor is Hamiltonian if and only if it is $2$-connected. We show furthermore that, if a Hamilton circle exists in such a graph, then it is unique and spanned by the $2$-contractible edges.\u00a0The third result of this paper is a construction of a graph which answers positively the question of Mohar whether regular infinite graphs with a unique Hamilton circle exist.<\/jats:p>","DOI":"10.37236\/6773","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:16:58Z","timestamp":1578669418000},"source":"Crossref","is-referenced-by-count":5,"title":["Hamiltonicity in Locally Finite Graphs: Two Extensions and a Counterexample"],"prefix":"10.37236","volume":"25","author":[{"given":"Karl","family":"Heuer","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,7,27]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i3p13\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i3p13\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:30:14Z","timestamp":1579235414000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i3p13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,27]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2018,7,12]]}},"URL":"https:\/\/doi.org\/10.37236\/6773","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,7,27]]},"article-number":"P3.13"}}