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2015 Knight's tours on boards with odd dimensions
Baoyue Bi, Steve Butler, Stephanie DeGraaf, Elizabeth Doebel
Involve 8(4): 615-627 (2015). DOI: 10.2140/involve.2015.8.615

Abstract

A closed knight’s tour of a board consists of a sequence of knight moves, where each square is visited exactly once and the sequence begins and ends with the same square. For boards of size m × n where m and n are odd, a tour is impossible because there are unequal numbers of white and black squares. By deleting a square, we can fix this disparity, and we determine which square to remove to allow for a closed knight’s tour.

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Baoyue Bi. Steve Butler. Stephanie DeGraaf. Elizabeth Doebel. "Knight's tours on boards with odd dimensions." Involve 8 (4) 615 - 627, 2015. https://doi.org/10.2140/involve.2015.8.615

Information

Received: 29 April 2014; Revised: 21 June 2014; Accepted: 2 August 2014; Published: 2015
First available in Project Euclid: 22 November 2017

zbMATH: 1316.05081
MathSciNet: MR3366013
Digital Object Identifier: 10.2140/involve.2015.8.615

Subjects:
Primary: 05C45
Secondary: 00A09

Rights: Copyright © 2015 Mathematical Sciences Publishers

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Vol.8 • No. 4 • 2015
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