  We present a new edge selection heuristic and vertex ordering heuristic that
together enable one to compute the Tutte polynomial of much larger sparse
graphs than was previously doable. As a specific example, we are able to
compute the Tutte polynomial of the truncated icosahedron graph using our Maple
implementation in under 4 minutes on a single CPU. This compares with a recent
result of Haggard, Pearce and Royle whose special purpose C++ software took one
week on 150 computers.
