, Volume 15, Issue 1, pp 1–10 | Cite as

The complexity of computing the tutte polynomial on transversal matroids

  • Charles J. Colbourn
  • J. Scott Provan
  • Dirk Vertigan


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.

Mathematics Subject Classification (1991)

05 D 15 68 Q 25 68 R 05 


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Copyright information

© Akadémiai Kiadó 1995

Authors and Affiliations

  • Charles J. Colbourn
    • 1
  • J. Scott Provan
    • 2
  • Dirk Vertigan
    • 3
  1. 1.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada
  2. 2.Department of Operations ResearchUniversity of North CarolinaChapel Hill
  3. 3.Department of MathematicsLouisiana State UniversityBaton Rouge

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