Define the cube graph as follows:
There are vertices, labelled . Draw an edge between and if and only if the binary representations of and differ in exactly one digit.
We would like to find a path along the cube graph that crosses each edge exactly once, and begins and ends at the same vertex. For this is possible: start at 0, move to 2, move to 3, move to 1, move back to 0.
What about for or