Knight's tours on rectangular chessboards using external squares
type: Item
instance of: scholarly article
title: Knight's tours on rectangular chessboards using external squares
zbMATH Open document ID: 1309.05083
DOI: 10.1155/2014/210892
author: Grady Bullington
author: Linda Eroh
author: Steven J. Winters
author: Garry Johns
published in: Journal of Discrete Mathematics
publication date: 2015-03-26T00:00:00Z
review text: Summary: 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 \(8 \times 8\) chessboard can easily be extended to rectangular boards, and \textit{A. Schwenk} [Math. Mag. 64, No. 5, 325--332 (1991; Zbl 0761.05041)] characterized all rectangular boards that have a closed knight's tour. More recently, \textit{J. Demaio} and \textit{T. Hippchen} [Math. Mag. 82, No. 3, 219--225 (2009; Zbl 1227.97064)] 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?
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C45
Mathematics Subject Classification ID: 97K20
zbMATH DE Number: 6419761
zbMATH Keywords: Hamiltonian cycles
zbMATH Keywords: bigraphs
zbMATH Keywords: tournaments
Wikidata QID: Q59048955
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/210892
OpenAlex ID: W1978508714
cites work: Q4821596
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description: scientific article; zbMATH DE number 6419761