Which Chessboards have a Closed Knight's Tour within the Rectangular Prism?

Which Rectangular Chessboards Have a Knight's Tour?

The Closed Knight Tour Problem in Higher Dimensions

The problem of existence of closed knight tours for rectangular chessboards was solved by Schwenk in 1991. Last year, in 2011, DeMaio and Mathew provide an extension of this result for 3-dimensional rectangular boards. In this article, we give the solution for n-dimensional rectangular boards, for n > 4.

Which Chessboards have a Closed Knight's Tour within the Cube?

A closed knight’s tour of a chessboard uses legal moves of the knight to visit every square exactly once and return to its starting position. When the chessboard is translated into graph theoretic terms the question is transformed into the existence of a Hamiltonian cycle. There are two common tours to consider on the cube. One is to tour the six exterior n × n boards that form the cube. The ot...

An Efficient Algorithm for the Knight's Tour Problem

A knight’s tour is a series of moves made by a knight visiting every square of an n x n chessboard exactly once. The knight’s tour problem is the problem of constructing such a tour, given n. A knight’s tour is called closed if the last square visited is also reachable from the first square by a knight’s move, and open otherwise. Define the knight’s graph for an n x n chessboard to be the graph...

Combinatorial Chessboard Rearrangements

Many problems concerning tilings of rectangular boards are of significant combinatorial interest. In this paper we introduce a similar type of counting problem based on game piece rearrangements. Many of these rearrangements satisfy recurrence relations which can be computed using various combinatorial techniques. We also present the solution to a rearrangement counterpart to the well–known kni...