Knight's tours on cylinders and other surfaces (Q2717912)
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scientific article; zbMATH DE number 1606012
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Knight's tours on cylinders and other surfaces |
scientific article; zbMATH DE number 1606012 |
Statements
19 June 2001
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Möbius strip
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chessboard
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knight's tour
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Klein bottle
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Knight's tours on cylinders and other surfaces (English)
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The paper considers \(m\times n\)-chessbords having two opposite sides identified directly (cylindrical chessboard) or identified conversely (Möbius chessboard) and characterizes in both cases those pairs of numbers \(m\) and \(n\), for which the chessboard has a knight's tour. This gives a new proof for the analogous result on the torus [see \textit{J. J. Watkins} and \textit{R. L. Hoenigman}, Math. Mag. 70, No. 3, 175-184 (1997; Zbl 0906.05041)] and settles also the case of the Klein bottle.
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