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
Contributeur : Eric Bourreau
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Soumis le : vendredi 31 octobre 2014 - 12:09:02
Dernière modification le : jeudi 24 mai 2018 - 15:59:21
Document(s) archivé(s) le : lundi 2 février 2015 - 16:28:37
