Computing representations of matroids of bounded branch-width

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. © Springer-Verlag Berlin Heidelberg 2007.