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The complexity of computing the tutte polynomial on transversal matroids

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Abstract

The complexity of computing the Tutte polynomialT(M,x,y) is determined for transversal matroidM and algebraic numbersx andy. It is shown that for fixedx andy the problem of computingT(M,x,y) forM a transversal matroid is #P-complete unless the numbersx andy satisfy (x−1)(y−1)=1, in which case it is polynomial-time computable. In particular, the problem of counting bases in a transversal matroid, and of counting various types of “matchable” sets of nodes in a bipartite graph, is #P-complete.

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Authors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Charles J. Colbourn

  2. Department of Operations Research, University of North Carolina, 27599-3180, Chapel Hill, North Carolina

    J. Scott Provan

  3. Department of Mathematics, Louisiana State University, 70803-4918, Baton Rouge, Louisiana

    Dirk Vertigan

Authors
  1. Charles J. Colbourn
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  2. J. Scott Provan
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  3. Dirk Vertigan
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Colbourn, C.J., Provan, J.S. & Vertigan, D. The complexity of computing the tutte polynomial on transversal matroids. Combinatorica 15, 1–10 (1995). https://doi.org/10.1007/BF01294456

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  • DOI: https://doi.org/10.1007/BF01294456

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