The closed knight tour problem in higher dimensions

Bruno Golenia (1) , Sylvain Golenia (2)

1 Computer Science Department [Bristol]
2 IMB - Institut de Mathématiques de Bordeaux

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. The closed knight tour problem in higher dimensions. 2012. ⟨hal-00673397v2⟩