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We present a new edge selection heuristic and vertex ordering heuristic thattogether enable one to compute the Tutte polynomial of much larger sparsegraphs than was previously doable. As a specific example, we are able tocompute the Tutte polynomial of the truncated icosahedron graph using our Mapleimplementation in under 4 minutes on a single CPU. This compares with a recentresult of Haggard, Pearce and Royle whose special purpose C++ software took oneweek on 150 computers.

A new edge selection heuristic for computing the Tutte polynomial of an undirected graph