The Closed Knight Tour Problem in Higher Dimensions

Joshua Erde, Bruno Golénia, Sylvain Golénia


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 $n\geq 4$.


Chessboard, Hamiltonian cycle

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