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.
- Mathematics Subject Classification (1991): 05D15, 68Q25, 68R05
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Computational Mathematics