On the Complexity of Computing the Tutte Polynomial of Bicircular Matroids

  • Authors:

  • Omer Giménez;Marc Noy

  • Affiliations:

  • Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Pau Gargallo 5, 08028 Barcelona, Spain (e-mail: omer.gimenez@upc.es, marc.noy@upc.es);Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Pau Gargallo 5, 08028 Barcelona, Spain (e-mail: omer.gimenez@upc.es, marc.noy@upc.es)

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 2006

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Abstract

We show that evaluating the Tutte polynomial for the class of bicircular matroids is #P-hard 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 $(x-1)(y-1)=1$.