Question: Show that a bipartite graph with an odd number of vertices does not have a Hamilton circuit.
A knight is a chess piece that can move either two spaces horizontally and one space vertically or one space horizontally and two spaces vertically. That is, a knight on square (x, y) can move to any of the eight squares (x ± 2, y ± 1), (x ± 1, y ± 2), if these squares are on the chessboard, as illustrated here.