*Bounty: 50*

*Bounty: 50*

The following is the Problem 1.4 in [1]:

**Finding an Eulerian path.** Show that if a connected graph has two vertices of odd degree and we start at one of them, Fleury’s algorithm will produce an Eulerian path, and that if all vertices have even degree, it (Fleury’s algorithm) will produce an Eulerian cycle no matter where we start.

Reference

[1] C. Moore and S. Mertens, *The Nature of Computation*, Oxford University Press, 2015.

I have tried to answer this question for a long time, but I don’t have any idea. By the way, this question is not my homework, I am just interested in solving this question.