The knight’s tour problem is a famous problem in chess and computer science which asks the following question: can we move the knight on an $n \ \times \ n$ chessboard such that it visits every square exactly once? The answer is yes iff $n\geq5$. Additionally, there are algorithms which can solve it in $O(n^2)$ […]

It is generally difficult to determine whether a (large) graph have no Hamilton cycle (As opposed to determining whether it has any Euler circuit). This example illustrates a method (which sometimes work) to indicate that a graph has no Hamilton cycle. a. Show that if m and n are odd integers (not both = 1), […]

The knight’s tour is a sequence of 64 squares on a chess board, where each square is visted once, and each subsequent square can be reached from the previous by a knight’s move. Tours can be cyclic, if the last square is a knight’s move away from the first, and acyclic otherwise. There are several […]

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