Abstract
For every k ≥ 1 and two finite fields \({\mathbb F}\) and \({\mathbb F}'\), we design a polynomial-time algorithm that given a matroid \({\mathcal M}\) of branch-width at most k represented over \({\mathbb F}\) decides whether \({\mathcal M}\) is representable over \({\mathbb F}'\) and if so, it computes a representation of \({\mathcal M}\) over \({\mathbb F}'\). The algorithm also counts the number of non-isomorphic representations of \({\mathcal M}\) over \({\mathbb F}'\). Moreover, it can be modified to list all such non-isomorphic representations.
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Král’, D. (2007). Computing Representations of Matroids of Bounded Branch-Width. In: Thomas, W., Weil, P. (eds) STACS 2007. STACS 2007. Lecture Notes in Computer Science, vol 4393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70918-3_20
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DOI: https://doi.org/10.1007/978-3-540-70918-3_20
Publisher Name: Springer, Berlin, Heidelberg
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