The Topology of Knight's Tours on Surfaces
Kara Teehan
Rutgers University
Abstract
We investigate the homotopy classes of closed knight’s tours on cylinders and tori. Specifically, we characterize the dimensions of cylindrical chessboards that admit closed knight’s tours realizing the identity of the fundamental group and those that admit closed tours realizing a generator of the fundamental group. We also produce analogous results for toroidal chessboards.
