{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:09Z","timestamp":1753893789799,"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>Let $G$ be a connected graph that is the edge-disjoint union of two paths of length $n$, where $n\\ge2$.  Using a result of Thomason on decompositions of 4-regular graphs into pairs of Hamiltonian cycles, we prove that $G$ has a third path of length $n$.<\/jats:p>","DOI":"10.37236\/1665","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:27:05Z","timestamp":1578709625000},"source":"Crossref","is-referenced-by-count":1,"title":["A Proof of the Two-path Conjecture"],"prefix":"10.37236","volume":"9","author":[{"given":"Herbert","family":"Fleischner","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert R.","family":"Molina","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ken W.","family":"Smith","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Douglas B.","family":"West","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2002,3,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v9i1n4\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v9i1n4\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:15:12Z","timestamp":1579324512000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v9i1n4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,3,13]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2002,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1665","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2002,3,13]]},"article-number":"N4"}}