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Computing Representations of Matroids of Bounded Branch-Width

  • Daniel Král’
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4393)

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.

Keywords

Linear Subspace Graph Transformation Computing Representation Tutte Polynomial Isomorphic Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Daniel Král’
    • 1
  1. 1.Institute for Theoretical Computer Science (ITI), Faculty of Mathematics and Physics, Charles University, Malostranské náměstí 25, 118 00 PragueCzech Republic

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