Generalised Euler's knight
Beldiceanu, Nicolas ; Bourreau, Eric ; Simonis, Helmut ; Aggoun, Abderrahmane
HAL, lirmm-01079127 / Harvested from HAL
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
Publié le : 1998-07-04
Classification:  [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],  [INFO.INFO-RO]Computer Science [cs]/Operations Research [cs.RO],  [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
@article{lirmm-01079127,
     author = {Beldiceanu, Nicolas and Bourreau, Eric and Simonis, Helmut and Aggoun, Abderrahmane},
     title = {Generalised Euler's knight},
     journal = {HAL},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/lirmm-01079127}
}
Beldiceanu, Nicolas; Bourreau, Eric; Simonis, Helmut; Aggoun, Abderrahmane. Generalised Euler's knight. HAL, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/lirmm-01079127/