Generalised Euler’s knight

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