Computing representations of matroids of bounded branch-width

Authors:
Daniel Král
Affiliations:
Institute for Theoretical Computer Science, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Venue:
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Year:
2007

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Abstract

For every k ≥ 1 and two finite fields F and F′, we design a polynomial-time algorithm that given a matroid M of branch-width at most k represented over F decides whether M is representable over F′ and if so, it computes a representation of M over F′. The algorithm also counts the number of non-isomorphic representations of M over F′. Moreover, it can be modified to list all such non-isomorphic representations.