An algorithm for the Tutte polynomials of graphs of bounded treewidth
Discrete Mathematics
Random Structures & Algorithms - Special issue on statistical physics methods in discrete probability, combinatorics, and theoretical computer science
Constructive Linear Time Algorithms for Branchwidth
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Evaluating the Tutte Polynomial for Graphs of Bounded Tree-Width
Combinatorics, Probability and Computing
Coloured Tutte polynomials and Kauffman brackets for graphs of bounded tree width
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
A Parametrized Algorithm for Matroid Branch-Width
SIAM Journal on Computing
Branch-width, parse trees, and monadic second-order logic for matroids
Journal of Combinatorial Theory Series B
On the Complexity of Computing the Tutte Polynomial of Bicircular Matroids
Combinatorics, Probability and Computing
Branch-width, parse trees, and monadic second-order logic for matroids
Journal of Combinatorial Theory Series B
Decomposition width of matroids
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Decomposition width of matroids
Discrete Applied Mathematics
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It is a classical result of Jaeger, Vertigan and Welsh that evaluating the Tutte polynomial of a graph is #P-hard in all but a few special points. On the other hand, several papers in the past few years have shown that the Tutte polynomial of a graph can be efficiently computed for graphs of bounded tree-width. In this paper we present a recursive formula computing the Tutte polynomial of a matroid $M$ represented over a finite field (which includes all graphic matroids), using a so called parse tree of a branch-decomposition of $M$. This formula provides an algorithm computing the Tutte polynomial for a representable matroid of bounded branch-width in polynomial time with a fixed exponent.