The Topology of Knight's Tours on Surfaces
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.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.