Decomposition Width of Matroids

  • Daniel Král’
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6198)

Abstract

Hliněný [J. Combin. Theory Ser. B 96 (2006), 325–351] showed that every matroid property expressible in the monadic second order logic can be decided in linear time for matroids with bounded branch-width that are represented over finite fields. To be able to extend these algorithmic results to matroids not representable over finite fields, we introduce a new matroid width parameter, the decomposition width, and show that every matroid property expressible in the monadic second order logic can be computed in linear time for matroids given by a decomposition with bounded width. We also relate the decomposition width to matroid branch-width and discuss implications of our results with respect to other known algorithms.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Daniel Král’
    • 1
  1. 1.Institute for Theoretical Computer Science (ITI) Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic

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