Generalised Knight's Tours
Abstract
The problem of existence of closed knight's tours in [n]d, where [n]=\0, 1, …, n-1\, was recently solved by Erde, Gol\'enia, and Gol\'enia. They raised the same question for a generalised, (a, b) knight, which is allowed to move along any two axes of [n]d by a and b unit lengths respectively. Given an even number a, we show that the [n]d grid admits an (a, 1) knight's tour for sufficiently large even side length n.
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