Twibet: a recursive solution in Ptyhon

Today a friend told me she's struggling with solving the EuroPython 2011 Problem D, called Twibet. I wrote a quick solution and I'm publishing it here for those who are curious about it.
The key to my solution was the recursive traversal (traverse_graph) of a directed graph. The representation of the graph is a dictionary of the monks as keys and a list of the following monks as values.
Because running on the large input file raised a runtime error of  maximum recursion depth exceeded, I used a this little hack: sys.setrecursionlimit(10000).
UPDATE: Here are the solutions of the contestants.