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Knight's Tours And Zeta Functions, Alfred James Brown

Master's Theses

Given an m × n chessboard, we get an associated graph by letting each square represent a vertex and by joining two vertices if there is a valid move by a knight between the corresponding squares. A knight’s tour is a sequence of moves in which the knight lands on every square exactly once, i.e., a Hamiltonian path on the associated graph. Knight’s tours have an interesting history. One interesting mistake regarding Knight’s Tours was made by the famous mathematician Euler. His mistake led to the further study of knight’s tours on 3 × n chessboards. We will explore and …