ICALP 2012: Automata, Languages, and Programming pp 239-250

# Deciding First Order Properties of Matroids

• Tomáš Gavenčiak
• Daniel Král
• Sang-il Oum
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7392)

## Abstract

Frick and Grohe [J. ACM 48 (2006), 1184–1206] introduced a notion of graph classes with locally bounded tree-width and established that every first order property can be decided in almost linear time in such a graph class. Here, we introduce an analogous notion for matroids (locally bounded branch-width) and show the existence of a fixed parameter algorithm for first order properties in classes of regular matroids with locally bounded branch-width. To obtain this result, we show that the problem of deciding the existence of a circuit of length at most k containing two given elements is fixed parameter tractable for regular matroids.

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## Copyright information

© Springer-Verlag Berlin Heidelberg 2012

## Authors and Affiliations

• Tomáš Gavenčiak
• 1
• Daniel Král
• 2
• 3
• Sang-il Oum
• 4
1. 1.Department of Applied Mathematics, Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic
2. 2.Department of MathematicsUniversity of West BohemiaPilsenCzech Republic
3. 3.Computer Science Institute, Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic
4. 4.Department of Mathematical SciencesKAISTDaejeonSouth Korea