eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-12-01
76:1
76:14
10.4230/LIPIcs.MFCS.2017.76
article
K4-free Graphs as a Free Algebra
Cosme Llópez, Enric
Pous, Damien
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol083-mfcs2017/LIPIcs.MFCS.2017.76/LIPIcs.MFCS.2017.76.pdf
Universal Algebra
Graph theory
Axiomatisation
Tree decompositions
Graph minors