The rook graph $G$ is a graph whose edges represent all the possible legal moves of the rook chess piece on a chessboard. The problem we consider is the following. Given any set $M$ containing pairs of cells such that each cell of the $m1 imes m2$ chessboard is in exactly one pair, we determine the values of the positive integers m1 and m2 for which it is possible to construct a closed tour of all the cells of the chessboard, that is a Hamiltonian cycle, which uses all the pairs of cells in $M$ and possible moves of the rook.

Saved by the rook

Marien Abreu;
2020-01-01

Abstract

The rook graph $G$ is a graph whose edges represent all the possible legal moves of the rook chess piece on a chessboard. The problem we consider is the following. Given any set $M$ containing pairs of cells such that each cell of the $m1 imes m2$ chessboard is in exactly one pair, we determine the values of the positive integers m1 and m2 for which it is possible to construct a closed tour of all the cells of the chessboard, that is a Hamiltonian cycle, which uses all the pairs of cells in $M$ and possible moves of the rook.
2020
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11563/144545
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