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CMSO-Transducing Tree-Like Graph Decompositions

Authors Rutger Campbell, Bruno Guillon, Mamadou Moustapha Kanté , Eun Jung Kim , Noleen Köhler

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Author Details

Rutger Campbell
  • Discrete Mathematics Group, Institute for Basic Science, Daejeon, South Korea
Bruno Guillon
  • Université Clermont Auvergne, Clermont Auvergne INP, LIMOS, CNRS, Clermont-Ferrand, France
Mamadou Moustapha Kanté
  • Université Clermont Auvergne, Clermont Auvergne INP, LIMOS, CNRS, Clermont-Ferrand, France
Eun Jung Kim
  • KAIST, Daejeon, South Korea
  • CNRS, France
Noleen Köhler
  • University of Leeds, UK

Funding

  • Campbell, Rutger: Supported by the Institute for Basic Science (IBS-R029-C1).
  • Kanté, Mamadou Moustapha: Supported by the French National Research Agency (ANR-18-CE40-0025-01 and ANR-20-CE48-0002).

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Rutger Campbell, Bruno Guillon, Mamadou Moustapha Kanté, Eun Jung Kim, and Noleen Köhler. CMSO-Transducing Tree-Like Graph Decompositions. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 22:1-22:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.STACS.2025.22

Abstract

We show that given a graph G we can CMSO-transduce its modular decomposition, its split decomposition and its bi-join decomposition. This improves results by Courcelle [Logical Methods in Computer Science, 2006] who gave such transductions using order-invariant MSO, a strictly more expressive logic than CMSO. Our methods more generally yield C_{2}MSO-transductions of the canonical decomposition of weakly-partitive set systems and weakly-bipartitive systems of bipartitions.

Subject Classification

ACM Subject Classification
  • Theory of computation → Finite Model Theory
Keywords
  • MSO-transduction
  • MSO-definability
  • graph decomposisions

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