Knight's Tours on Rectangular Chessboards Using External Squares. (8th December 2014)

• Record Type: Journal Article
• Authors: Bullington, Grady; Eroh, Linda; Winters, Steven J.; Johns, Garry L.
• Other Names: Nikolopoulos Stavros D. Academic Editor.
• Is Part Of: Journal of discrete mathematics. Volume 2014(2014)
• Publication Date: 2014-12-08
• Subjects: Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Periodicals; 511.1
• DOI: 10.1155/2014/210892
• Languages: English
• ISSNs: 2090-9837

Abstract

Abstract : 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?