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Treewidth-Two Graphs as a Free Algebra

Authors Christian Doczkal, Damien Pous

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  • Mathematics of computing → Graph theory
  • Theory of computation → Rewrite systems
  • Computing methodologies → Symbolic and algebraic manipulation
Keywords
  • Treewidth
  • Universal Algebra
  • Rewriting

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Abstract

We give a new and elementary proof that the graphs of treewidth at most two can be seen as a free algebra. This result was originally established through an elaborate analysis of the structure of K_4-free graphs, ultimately reproving the well-known fact that the graphs of treewidth at most two are precisely those excluding K_4 as a minor. Our new proof is based on a confluent and terminating rewriting system for term-labeled graphs and does not involve graph minors anymore. The new strategy is simpler and robust in the sense that it can be adapted to subclasses of treewidth-two graphs, e.g., graphs without self-loops.

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Christian Doczkal and Damien Pous. Treewidth-Two Graphs as a Free Algebra. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 60:1-60:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.MFCS.2018.60

Author Details

Christian Doczkal
  • Univ Lyon, CNRS, ENS de Lyon, UCB Lyon 1, LIP, France
Damien Pous
  • Univ Lyon, CNRS, ENS de Lyon, UCB Lyon 1, LIP, France

Funding

This work has been funded by the European Research Council (ERC) under the European Union’s Horizon 2020 programme (CoVeCe, grant agreement No 678157). This work was supported by the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program "Investissements d'Avenir" (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR).

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