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