Geodesic
The closed knight tour problem in higher dimensions
Joshua Erde1 ; Bruno Golénia2 ; Sylvain Golénia3
1Department of Pure Mathematics and Mathematical Statistics, Center for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WB, United Kingdom
2Department of Computer Science, University of Bristol, Merchant Venturers Building, Woodland Road BRISTOL BS8 1UB, United Kingdom
3Institut de Mathématiques de Bordeaux Université Bordeaux 1 351, cours de la Libération F-33405 Talence cedex
The electronic journal of combinatorics, Tome 19 (2012) no. 4
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The problem of existence of closed knight tours for rectangular chessboards was solved by Schwenk in 1991. Last year, in 2011, DeMaio and Mathew provide an extension of this result for $3$-dimensional rectangular boards. In this article, we give the solution for $n$-dimensional rectangular boards, for $n\geq 4$.
DOI : 10.37236/2272
Classification : 05C45, 00A08
Mots-clés : chessboard, Hamiltonian cycle, closed knight tours, n-dimensional rectangular chessboard

Joshua Erde  1   ; Bruno Golénia  2   ; Sylvain Golénia  3

1 Department of Pure Mathematics and Mathematical Statistics, Center for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WB, United Kingdom
2 Department of Computer Science, University of Bristol, Merchant Venturers Building, Woodland Road BRISTOL BS8 1UB, United Kingdom
3 Institut de Mathématiques de Bordeaux Université Bordeaux 1 351, cours de la Libération F-33405 Talence cedex 
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     author = {Joshua Erde and Bruno Gol\'enia and Sylvain Gol\'enia},
     title = {The closed knight tour problem in higher dimensions},
     journal = {The electronic journal of combinatorics},
     year = {2012},
     volume = {19},
     number = {4},
     doi = {10.37236/2272},
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}
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Joshua Erde; Bruno Golénia; Sylvain Golénia. The closed knight tour problem in higher dimensions. The electronic journal of combinatorics, Tome 19 (2012) no. 4. doi: 10.37236/2272

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