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On Matroid Representability and Minor Problems

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Mathematical Foundations of Computer Science 2006 (MFCS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4162))

Abstract

In this paper we look at complexity aspects of the following problem (matroid representability) which seems to play an important role in structural matroid theory: Given a rational matrix representing the matroid M, the question is whether M can be represented also over another specific finite field. We prove this problem is hard, and so is the related problem of minor testing in rational matroids. The results hold even if we restrict to matroids of branch-width three.

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Author information

Authors and Affiliations

  1. Faculty of Informatics, Masaryk University in Brno, Botanická 68a, 602 00, Brno, Czech Republic

    Petr Hliněný

  2. Department of Computer Science, VŠB – Technical University Ostrava, 17. listopadu 15, 708 33, Ostrava, Czech Republic

    Petr Hliněný

Authors
  1. Petr Hliněný
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Comenius University, Mlynská dolina, 84248, Bratislava, Slovakia

    Rastislav Královič

  2. Institute of Informatics, University of Warsaw, Poland

    Paweł Urzyczyn

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© 2006 Springer-Verlag Berlin Heidelberg

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Hliněný, P. (2006). On Matroid Representability and Minor Problems. In: Královič, R., Urzyczyn, P. (eds) Mathematical Foundations of Computer Science 2006. MFCS 2006. Lecture Notes in Computer Science, vol 4162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11821069_44

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  • DOI: https://doi.org/10.1007/11821069_44

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-37791-7

  • Online ISBN: 978-3-540-37793-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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