{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T11:14:11Z","timestamp":1697886851372},"reference-count":3,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,3]],"date-time":"2006-10-03T00:00:00Z","timestamp":1159833600000},"content-version":"vor","delay-in-days":8067,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1984,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>K<\/jats:italic> be the 1\u2010skeleton of the regular tessellation of Euclidean <jats:italic>n<\/jats:italic>\u2010space by <jats:italic>n<\/jats:italic>\u2010cubes, <jats:italic>n<\/jats:italic> \u2265 2. We show that <jats:italic>K<\/jats:italic> admits <jats:italic>a doubly Eulerian trail<\/jats:italic> (<jats:italic>simply Eulerian trail<\/jats:italic>), that is, a doubly infinite path \u03c0 = \u2026 <jats:italic>e<\/jats:italic><jats:sub>\u22121<\/jats:sub><jats:italic>e<\/jats:italic><jats:sub>0<\/jats:sub><jats:italic>e<\/jats:italic><jats:sub>1<\/jats:sub> \u2026 where, out of each pair {<jats:italic>e, e<\/jats:italic><jats:sup>\u22121<\/jats:sup>} of oppositely directed edges, both (exactly one) appear(s) exactly once in \u03c0, and where no <jats:italic>e<\/jats:italic><jats:sub>i+1<\/jats:sub> = <jats:italic>e<\/jats:italic><jats:sub>i<\/jats:sub><jats:sup>\u22121<\/jats:sup> (there are no U\u2010turns).<\/jats:p>","DOI":"10.1002\/jgt.3190080306","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T11:20:52Z","timestamp":1180178452000},"page":"379-385","source":"Crossref","is-referenced-by-count":2,"title":["Doubly eulerian trails on rectangular grids"],"prefix":"10.1002","volume":"8","author":[{"given":"J. L.","family":"Brenner","sequence":"first","affiliation":[]},{"given":"R. C.","family":"Lyndon","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,3]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1983.104.285"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(83)90245-5"},{"issue":"1736","key":"e_1_2_1_4_2","first-page":"126","article-title":"Solutio problematis ad geometriam situs pertinentis","volume":"8","author":"Euler L.","journal-title":"Comm. Acad. Sci. I. Petropolitanae"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190080306","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190080306","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,20]],"date-time":"2023-10-20T12:20:15Z","timestamp":1697804415000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190080306"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1984,9]]},"references-count":3,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1984,9]]}},"alternative-id":["10.1002\/jgt.3190080306"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190080306","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1984,9]]}}}