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2024 | OriginalPaper | Chapter

The Existence of a Knight’s Tour on the Surface of Rectangular Boxes

Authors : Shengwei Lu, Carl Yerger

Published in: Combinatorics, Graph Theory and Computing

Publisher: Springer Nature Switzerland

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Abstract

A knight’s tour is a sequence of knight’s moves such that each square on the board is visited exactly once. In this chapter, we show that a closed knight’s tour exists on the surface of a rectangular box of any size. Our general algorithm is to concatenate the top and bottom faces of a box with its side faces. When general criteria are not satisfied, especially when the dimensions of the rectangular box are small, we devise some special techniques to cover these cases.

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previous chapter Production Matrices of Double Riordan Arrays
next chapter A New Upper Bound for the Site Percolation Threshold of the Square Lattice
Literature
1.
B. Bi, S. Butler, S. DeGraaf and E. Doebel, Knight’s Tours on Boards with Odd Dimensions, Involve, 8 (2015), 615–627.MathSciNetCrossRef
2.
3.
4.
A. Kumar, A Study of Knight’s Tours on the Surface of a Cube, Crux Mathematicorum with Mathematical Mayhem, 35 (2000), 313–319.
5.
H. J. R. Murray, A History of Chess, Oxford University Press, London (1913).
6.
Y. Qing, J. J. Watkins, Knight’s Tours for Cubes and Boxes, Congressus Numerantium, 181 (2006), 41–49.MathSciNet
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8.
K. Seibel, The Knight’s Tour on the Cylinder and Torus, REU paper, Oregon State University (1994).
9.
H. C. Warnsdorff, Des Rösselsprunges einfachste und allgemeinste Lösung, Schmalkalden (1823).
10.
J. J. Watkins, Across the Board: The Mathematics of Chessboard Problems, Princeton University Press (2004).
Metadata
Title
The Existence of a Knight’s Tour on the Surface of Rectangular Boxes
Authors
Shengwei Lu
Carl Yerger
Copyright Year
2024
Book
Combinatorics, Graph Theory and Computing

Print ISBN: 978-3-031-62165-9

Electronic ISBN: 978-3-031-62166-6

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-62166-6_8

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