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), a Knight is not in Following features visit all the squares on an m × n 'chessboard' just once, return to the starting point. (A knight goes in a move two squares forward and one to the side.)
b. Show the same thing for a board of size 4 × n, n integer.
I know when is a hamilton cycle we visit every vertirce in the graph. I draw this in paint but i was very weird?? Somebody with a hint?