Knight's Tour - Oregon State University

Figure AFigure BThis construction can be done in polynomial time.Theorem 4.9 If there is a Hamiltonian path on the grid graph, then there is a knight’s touron the constructed chessboard.Proof. Given a grid graph and a Hamiltonian path, construct the chessboard. Theknight’s tour follows the Hamiltonian path on the grid graph. Using the boards below, toureach node starting in one corner and leaving through another. In this way the whole boardcan be toured in the order given by the Hamiltonian path on the grid graph.147