{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:11Z","timestamp":1753893791616,"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>A bent Hamilton cycle in a grid graph is one in which each edge in a successive pair of edges lies in a different dimension. We show that the $d$-dimensional grid graph has a bent Hamilton cycle if some dimension is even and $d \\geq 3$, and does not have a bent Hamilton cycle if all dimensions are odd. In the latter case, we determine the conditions for when a bent Hamilton path exists. For the $d$-dimensional toroidal grid graph (i.e., the graph product of $d$ cycles), we show that there exists a bent Hamilton cycle when all dimensions are odd and $d \\geq 3$. We also show that if $d=2$, then there exists a bent Hamilton cycle if and only if both dimensions are even.<\/jats:p>","DOI":"10.37236\/1694","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:30:08Z","timestamp":1578691808000},"source":"Crossref","is-referenced-by-count":7,"title":["Bent Hamilton Cycles in $d$-Dimensional Grid Graphs"],"prefix":"10.37236","volume":"10","author":[{"given":"F.","family":"Ruskey","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joe","family":"Sawada","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2003,1,6]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v10i1r1\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v10i1r1\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T00:10:36Z","timestamp":1579306236000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v10i1r1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,1,6]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2003,1,6]]}},"URL":"https:\/\/doi.org\/10.37236\/1694","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2003,1,6]]},"article-number":"R1"}}