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A Hamiltonian graph (directed or undirected) is a graph that contains a Hamiltonian cycle, that is, a cycle that visits every vertex exactly once.

19 votes
1 answer
1k views

Knight's tours in higher dimensions

I wonder if Knight's Tours have been explored in higher dimensions, using the following definition of a knight move. In dimension $d=2$, the knight moves left/right and forward/back one step and two …
Joseph O'Rourke's user avatar
8 votes
2 answers
591 views

Orthogonal Hamiltonian cycles in (n x n x n) grids

Let $C_n$ be a cubical $n \times n \times n$ subset of the integer lattice, so consisting of $n^3$ vertices. I am interested in special Hamiltonian cycles in $C_n$, special in the sense that (a) each …
Joseph O'Rourke's user avatar