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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 …
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 …