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Amalgam Width of Matroids

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Parameterized and Exact Computation (IPEC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8246))

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Abstract

We introduce a new matroid width parameter based on the operation of matroid amalgamation called amalgam-width. The parameter is linearly related to branch-width on finitely representable matroids, while still allowing algorithmic applications on non-representable matroids (which is not possible for branch-width). In particular, any property expressible in the monadic second order logic can be decided in linear time for matroids with bounded amalgam-width. We also prove that the Tutte polynomial can be computed in polynomial time for matroids with bounded amalgam-width.

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Author information

Authors and Affiliations

  1. DIMAP and Department of Computer Science, University of Warwick, Coventry, United Kingdom

    Lukáš Mach

  2. Computer Science Institute, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic

    Tomáš Toufar

Authors
  1. Lukáš Mach
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  2. Tomáš Toufar
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Editor information

Editors and Affiliations

  1. Royal Holloway, University of London, Egham Hill, TW20 0EX, Egham, UK

    Gregory Gutin

  2. Institute of Information Systems, Vienna University of Technology, (184/3), Favoritenstraße 9-11, 1040, Vienna, Austria

    Stefan Szeider

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© 2013 Springer International Publishing Switzerland

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Mach, L., Toufar, T. (2013). Amalgam Width of Matroids. In: Gutin, G., Szeider, S. (eds) Parameterized and Exact Computation. IPEC 2013. Lecture Notes in Computer Science, vol 8246. Springer, Cham. https://doi.org/10.1007/978-3-319-03898-8_23

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  • DOI: https://doi.org/10.1007/978-3-319-03898-8_23

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03897-1

  • Online ISBN: 978-3-319-03898-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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