Which rectangular chessboards have a knight's tour?
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...
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| Main Authors: | , |
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| Format: | text |
| Language: | English |
| Published: |
Animo Repository
1993
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| Subjects: | |
| Online Access: | https://animorepository.dlsu.edu.ph/etd_bachelors/16119 |
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| Institution: | De La Salle University |
| Language: | English |
| 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. |
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