Which rectangular chessboards have a knight's tour?
Date of Publication
1993
Document Type
Bachelor's Thesis
Degree Name
Bachelor of Science in Mathematics
College
College of Science
Department/Unit
Mathematics and Statistics
Abstract/Summary
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.
Abstract Format
html
Language
English
Format
Accession Number
TU06289
Shelf Location
Archives, The Learning Commons, 12F, Henry Sy Sr. Hall
Physical Description
51 leaves
Keywords
Board games; Chess; Knight (Chess); Mathematical recreations; Graph theory; Games
Recommended Citation
Laureola, L. M., & Monzon, A. B. (1993). Which rectangular chessboards have a knight's tour?. Retrieved from https://animorepository.dlsu.edu.ph/etd_bachelors/16119