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Recognizability equals monadic second-order definability for sets of graphs of bounded tree-width

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STACS 98 (STACS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1373))

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Abstract

We prove that for each k, there exists a MSO-transduction that associates with every graph of tree-width at most k one of its tree-decompositions of width at most k. Courcelle proves in (The Monadic second-order logic of graphs, I: Recognizable sets of finite graphs) that every set of graphs is recognizable if it is definable in Counting Monadic Second-Order logic. It follows that every set of graphs of bounded tree-width is CMSO-definable if and only if it is recognizable.

Research partly supported by the EC TMR Network GETGRATS (General Theory of Graph Transformation Systems) through the Universities of Bremen and Leiden.

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Authors and Affiliations

  1. LaBRI (CNRS Laboratory no 1304), Bordeaux-I University, 351 cours de la Libération, 33405, Talence, France

    Denis Lapoire

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  1. Denis Lapoire
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Michel Morvan Christoph Meinel Daniel Krob

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© 1998 Springer-Verlag

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Lapoire, D. (1998). Recognizability equals monadic second-order definability for sets of graphs of bounded tree-width. In: Morvan, M., Meinel, C., Krob, D. (eds) STACS 98. STACS 1998. Lecture Notes in Computer Science, vol 1373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028596

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  • DOI: https://doi.org/10.1007/BFb0028596

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64230-5

  • Online ISBN: 978-3-540-69705-3

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