Postman problem and graph theory

The Chinese Postman Problem: A postman departs from the post office, traverses every street in his assigned area, and then returns to the post office. He may walk along any street multiple times but must choose the shortest possible route.

Theorem
A necessary and sufficient condition for traversing all edges exactly once and returning to the starting point is that the number of edges connected to each vertex must be even; in other words, all vertices must be even vertices.