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Closed Knight's Tours With Minimal Square Removal For All Rectangular Boards, Joseph Demaio, Thomas Hippchen
Closed Knight's Tours With Minimal Square Removal For All Rectangular Boards, Joseph Demaio, Thomas Hippchen
Faculty Articles
A closed knight's tour of a chessboard uses legal moves of the knight to visit every square exactly once and return to its starting position. In 1991 Schwenk completely classified the rectangular chessboards that admit a closed knight's tour. For a rectangular chessboard that does not contain a closed knight's tour, this paper determines the minimum number of squares that must be removed in order to admit a closed knight's tour. Furthermore, constructions that generate a closed tour once appropriate squares are removed are provided.