The complexity of computing the tutte polynomial on transversal matroids

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

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

The complexity of computing the Tutte polynomial T(M, x,y) is determined for transversal matroid M and algebraic numbers x and y. It is shown that for fixed x and y the problem of computing T(M, x,y) for M a transversal matroid is #P-complete unless the numbers x and y 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.

Original languageEnglish (US)
Pages (from-to)1-10
Number of pages10
JournalCombinatorica
Volume15
Issue number1
DOIs
StatePublished - Mar 1 1995
Externally publishedYes

Keywords

  • Mathematics Subject Classification (1991): 05D15, 68Q25, 68R05

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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