English

Knight's Tours in Higher Dimensions

Combinatorics 2012-02-27 v1 Discrete Mathematics

Abstract

In this paper we are concerned with knight's tours on high-dimensional boards. Our main aim is to show that on the dd-dimensional board [n]d[n]^d, with nn even, there is always a knight's tour provided that nn is sufficiently large. In fact, we give an exact classification of the grids [n1]×...×[nd][n_1] \times ... \times [n_d] in which there is a knight's tour. This answers questions of DeMaio, DeMaio and Mathew, and Watkins.

Cite

@article{arxiv.1202.5548,
  title  = {Knight's Tours in Higher Dimensions},
  author = {Joshua Erde},
  journal= {arXiv preprint arXiv:1202.5548},
  year   = {2012}
}
R2 v1 2026-06-21T20:24:46.741Z