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

Print

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

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