Knight’s Tours on Rectangular Chessboards Using External Squares

Autor: Linda Eroh, Steven J. Winters, Grady D. Bullington, Garry L. Johns
Rok vydání: 2014
Předmět:
Zdroj: Journal of Discrete Mathematics. 2014:1-9
ISSN: 2090-9845
2090-9837
DOI: 10.1155/2014/210892
Popis: The classic puzzle of finding a closed knight’s tour on a chessboard consists of moving a knight from square to square in such a way that it lands on every square once and returns to its starting point. The 8 × 8 chessboard can easily be extended to rectangular boards, and in 1991, A. Schwenk characterized all rectangular boards that have a closed knight’s tour. More recently, Demaio and Hippchen investigated the impossible boards and determined the fewest number of squares that must be removed from a rectangular board so that the remaining board has a closed knight’s tour. In this paper we define an extended closed knight’s tour for a rectangular chessboard as a closed knight’s tour that includes all squares of the board and possibly additional squares beyond the boundaries of the board and answer the following question: how many squares must be added to a rectangular chessboard so that the new board has a closed knight’s tour?
Databáze: OpenAIRE
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