The closed knight tour problem in higher dimensions

Bruno Golenia (1) , Sylvain Golenia (2) , Joshua Erde (3)

1 Computer Science Department [Bristol]
2 IMB - Institut de Mathématiques de Bordeaux
3 DPMMS - Department of Pure Mathematics and Mathematical Statistics

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 $n\geq 4$.

Mots clés: Chessboard; Hamiltonian cycle

Domaines: Combinatoire [math.CO]

Bruno Golenia, Sylvain Golenia, Joshua Erde. The closed knight tour problem in higher dimensions. The Electronic Journal of Combinatorics, 2012, pp.Volume 19, Issue 4. ⟨hal-00673397v3⟩