A closed -knight’s tour on some cylinder chessboards

Abstract

A -knight’s move on the cylinder chessboard is the move of the knight 2 squares vertically or 2 squares horizontally and then 3 squares perpendicular to it. In this paper, we show a closed -knight’s tour on the cylinder chessboard for all positive integers and , and a closed -knight’s tour on the cylinder chessboard for all positive integers and . Moreover, we show that there is no closed -knight’s tours on the cylinder chessboard where (i) and (ii) and .

Keywords

• closed -knight’s tour
• cylinder chessboard
• hamiltonian cycle