K4-free Graphs as a Free Algebra

Authors Enric Cosme Llópez, Damien Pous

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Enric Cosme Llópez
Damien Pous

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Enric Cosme Llópez and Damien Pous. K4-free Graphs as a Free Algebra. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 76:1-76:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


Graphs of treewidth at most two are the ones excluding the clique with four vertices as a minor. Equivalently, they are the graphs whose biconnected components are series-parallel. We turn those graphs into a free algebra, answering positively a question by Courcelle and Engelfriet, in the case of treewidth two. First we propose a syntax for denoting them: in addition to series and parallel compositions, it suffices to consider the neutral elements of those operations and a unary transpose operation. Then we give a finite equational presentation and we prove it complete: two terms from the syntax are congruent if and only if they denote the same graph.
  • Universal Algebra
  • Graph theory
  • Axiomatisation
  • Tree decompositions
  • Graph minors


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