Which rectangular chessboards have a knight's tour?

• Main Authors: Laureola, Lorenz M., Monzon, Arturo B.
• Format: text
• Language: English
• Published: Animo Repository 1993
• Subjects: Board games; Chess; Knight (Chess); Mathematical recreations; Graph theory; Games
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16119
• Institution: De La Salle University

This study will try to determine which chessboards can hold a knight's tour. A knight's tour is formed when a knight, starting from any point on the board, visits each cell exactly once and ends on the starting cell using knight moves--usual moves of a knight in chess. To solve the problem, we construct a graph G(m,n), where m and n are positive integers, wherein the square cells of a chessboard are represented by the vertices of the graph. Two vertices are joined by an edge if there exists a knight move from one to the other. In Graph Theory, a knight's tour is equivalent to a Hamiltonian cycle. Extension of existing tours in G(m,n) too G(m,n+4) are shown in the paper together with nine examples of knight's tours on different sized graphs necessary for the solution.