The Tutte Polynomial for Matroids of Bounded Branch-Width

Warning

This publication doesn't include Faculty of Arts. It includes Faculty of Informatics. Official publication website can be found on muni.cz.
Authors

HLINĚNÝ Petr

Year of publication 2006
Type Article in Periodical
Magazine / Source Combin. Prob. Computing
MU Faculty or unit

Faculty of Informatics

Citation
Web
Field General mathematics
Keywords representable matroid; Tutte polynomial; branch-width;
Description It is a classical result of Jaeger, Vertigan and Welsh that evaluating the Tutte polynomial of a graph is $\#P$-hard in all but few special points. On the other hand, several papers in past 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 $\md M$ represented over a finite field (which includes all graphic matroids), using a so called parse tree of a branch-decomposition of $\md M$. This formula provides an algorithm computing the Tutte polynomial for a representable matroid of bounded branch-width in polynomial time with a fixed exponent.
Related projects:

You are running an old browser version. We recommend updating your browser to its latest version.