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K4-free Graphs as a Free Algebra


Graphs of treewidth at most two are the ones excluding the clique with four vertices (K4) as a minor, or equivalently, the graphs whose biconnected components are series-parallel. We turn those graphs into a finitely presented free algebra, answering positively a question by Courcelle and Engelfriet, in the case of treewidth two. First we propose a syntax for denoting these graphs: in addition to parallel composition and series composition, 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.
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Dates and versions

hal-01515752 , version 1 (28-04-2017)
hal-01515752 , version 2 (06-02-2018)


  • HAL Id : hal-01515752 , version 2


Enric Cosme-Llópez, Damien Pous. K4-free Graphs as a Free Algebra. 42nd International Symposium on Mathematical Foundations of Computer Science, Aug 2017, Aalborg, Denmark. ⟨hal-01515752v2⟩
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