Verbose Motivation for this Question Inspired by this paper about how the problem of counting unlabelled subtrees that are unique up to isomorphism is #P-complete, I was thinking about the problem for the specific case of caterpillar graphs. (a caterpillar graph, $C$, will become a path graph, $...

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 Euler...