On the Complexity of Computing the Tutte Polynomial of Bicircular Matroids

We show that evaluating the Tutte polynomial for the class of bicircular matroids is #Phard at every point (x, y) except those in the hyperbola (x − 1)(y − 1) = 1 and possibly those on the lines x = 0 and x = −1. Since bicircular matroids form a rather restricted subclass of transversal matroids, our results can be seen as a partial strengthening of a result by Colbourn, Provan and Vertigan, namely that the evaluation of the Tutte polynomial for the class of transversal matroids is #P-hard for all points except those in the hyperbola (x− 1)(y − 1) = 1.