The Tutte Polynomial for Matroids of Bounded Branch-Width

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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	doi http://journals.cambridge.org/action/displayJournal?jid=CPC
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:	Institute for Theoretical Computer Science