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Knight's tours on
boards with odd dimensions
Baoyue Bi, Steve Butler, Stephanie DeGraaf and Elizabeth Doebel
Vol. 8 (2015), No. 4, 615–627
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Abstract |
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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 where and 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. |
Keywords
knight's tour, expanders, chess boards
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Mathematical Subject Classification 2010
Primary: 05C45
Secondary: 00A09
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Milestones
Received: 29 April 2014
Revised: 21 June 2014
Accepted: 2 August 2014
Published: 23 June 2015
Communicated by Kenneth S. Berenhaut
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Authors |
| Baoyue Bi | |
| Department of Mathematics Iowa State University Ames, IA 50011 United States |
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| Steve Butler | |
| Department of Mathematics Iowa State University Ames, IA 50011 United States |
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| Stephanie DeGraaf | |
| Department of Mathematics Iowa State University Ames, IA 50011 United States |
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| Elizabeth Doebel | |
| Department of Mathematics Iowa State University Ames, IA 50011 United States |
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