{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:36Z","timestamp":1753893816991,"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>Marco Buratti has conjectured that, given an odd prime $p$ and a multiset $L$ containing $p-1$ integers taken from $\\{1,\\ldots,(p-1)\/2\\}$, there exists a Hamiltonian path in the complete graph with $p$ vertices whose multiset of edge-lengths is equal to $L$ modulo $p$. We give a positive answer to this conjecture in the case of multisets of the type $\\{1^a,2^b,3^c\\}$ by completely classifying such multisets that are linearly or cyclically realizable.<\/jats:p>","DOI":"10.37236\/316","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:16:00Z","timestamp":1578716160000},"source":"Crossref","is-referenced-by-count":10,"title":["Hamiltonian Paths in the Complete Graph with Edge-Lengths 1, 2, 3"],"prefix":"10.37236","volume":"17","author":[{"given":"Stefano","family":"Capparelli","sequence":"first","affiliation":[]},{"given":"Alberto Del","family":"Fra","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,3,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r44\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r44\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:57:39Z","timestamp":1579305459000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r44"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,3,15]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/316","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2010,3,15]]},"article-number":"R44"}}