Generalised Euler's knight

Nicolas Beldiceanu (1, 2) , Eric Bourreau (2) , Helmut Simonis (3, 2) , Abderrahmane Aggoun (2)

1 LINA - Laboratoire d'Informatique de Nantes Atlantique
2 COSYSTEC SA [Orsay]
3 4C UCC - Cork Constraint Computation Centre

Euler, Vandermonde, Dudeney, Schwesk, Berliner, Conrad and many others already considered knight's tours on chessboards. The classical knight's tour problem consist of finding out on a N × M chessboard a sequence of legal knight moves that visit every cell exactly once and finish by returning to the initial cell. A more challenging question is to generalise the problem to more than one knight. More precisely, we search for a partitioning of the m x n chessboard by a set of C cycles in such a way that each cell belongs to one single cycle. Moreover we impose all the cycles to be balanced. Since a cycle can't have an odd number of cells, we enforce that each cycle visits between 2 x floor(floor((m x n) / c) / 2) and 2 x cell(cell((m x n) / c) / 2) cells. We systematically consider all the boards m x n such that 1

Domaines: Combinatoire [math.CO]; Recherche opérationnelle [math.OC]; Mathématique discrète [cs.DM]

Nicolas Beldiceanu, Eric Bourreau, Helmut Simonis, Abderrahmane Aggoun. Generalised Euler's knight. 1998. ⟨lirmm-01079127⟩