{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:22Z","timestamp":1753893802021,"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>Every connected simple graph $G$ has an acyclic orientation. Define a graph ${AO}(G)$ whose vertices are the acyclic orientations of $G$ and whose edges join orientations that differ by reversing the direction of a single edge. It was known previously that ${AO}(G)$ is connected but not necessarily Hamiltonian. However, Squire  proved that the square ${AO}(G)^2$ is Hamiltonian. We prove the slightly stronger result that the prism ${AO}(G) \\times e$ is Hamiltonian. If $G$ is a mixed graph (some edges directed, but not necessarily all), then ${AO}(G)$ can be defined as before. The graph ${AO}(G)$ is again connected but we give examples showing that the prism is not necessarily Hamiltonian.<\/jats:p>","DOI":"10.37236\/1199","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:26:16Z","timestamp":1578687976000},"source":"Crossref","is-referenced-by-count":4,"title":["The Prism of the Acyclic Orientation Graph is Hamiltonian"],"prefix":"10.37236","volume":"2","author":[{"given":"Gara","family":"Pruesse","sequence":"first","affiliation":[]},{"given":"Frank","family":"Ruskey","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1995,3,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v2i1r5\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v2i1r5\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:32:25Z","timestamp":1579321945000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v2i1r5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,3,13]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1995,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1199","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1995,3,13]]},"article-number":"R5"}}