The complexity of computing the tutte polynomial on transversal matroids

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

doi:10.1007/BF01294456

The complexity of computing the tutte polynomial on transversal matroids

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

Research output: Contribution to journal › Article › peer-review

23 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 language	English (US)
Pages (from-to)	1-10
Number of pages	10
Journal	Combinatorica
Volume	15
Issue number	1
DOIs	https://doi.org/10.1007/BF01294456
State	Published - Mar 1995
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Computational Mathematics

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10.1007/BF01294456

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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.",

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N2 - 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.

AB - 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.

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The complexity of computing the tutte polynomial on transversal matroids

Abstract

Keywords

ASJC Scopus subject areas

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