Vol. 8, No. 4, 2015

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ISSN: 1944-4184 (e-only)
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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
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.

Keywords
knight's tour, expanders, chess boards
Mathematical Subject Classification 2010
Primary: 05C45
Secondary: 00A09
Milestones
Received: 29 April 2014
Revised: 21 June 2014
Accepted: 2 August 2014
Published: 23 June 2015

Communicated by Kenneth S. Berenhaut
Authors
Baoyue Bi
Department of Mathematics
Iowa State University
Ames, IA 50011
United States
Steve Butler
Department of Mathematics
Iowa State University
Ames, IA 50011
United States
Stephanie DeGraaf
Department of Mathematics
Iowa State University
Ames, IA 50011
United States
Elizabeth Doebel
Department of Mathematics
Iowa State University
Ames, IA 50011
United States