English

On Crosspatch Knight's Tours

Combinatorics 2013-10-15 v1

Abstract

A knight's tour is often represented as a broken line connecting the centers of successively visited squares. We say that two knight moves form a cross if the midpoints of their respective segments coincide. We show that no knight tour exists on a rectangular board in which every move is part of a cross. We also establish the general structure of pseudotours with this property.

Cite

@article{arxiv.1310.3450,
  title  = {On Crosspatch Knight's Tours},
  author = {Nikolai Beluhov},
  journal= {arXiv preprint arXiv:1310.3450},
  year   = {2013}
}

Comments

7 pages, 6 figures

R2 v1 2026-06-22T01:45:51.133Z