Abstract : 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
https://hal-lirmm.ccsd.cnrs.fr/lirmm-01079127
Contributor : Eric Bourreau
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Submitted on : Friday, October 31, 2014 - 12:09:02 PM
Last modification on : Thursday, May 24, 2018 - 3:59:21 PM
Long-term archiving on : Monday, February 2, 2015 - 4:28:37 PM
