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DOI: 10.4230/LIPIcs.MFCS.2017.76

K4-free Graphs as a Free Algebra

Authors: Enric Cosme Llópez and Damien Pous

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Abstract

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.

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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)

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@InProceedings{cosmellopez_et_al:LIPIcs.MFCS.2017.76,
  author =	{Cosme Ll\'{o}pez, Enric and Pous, Damien},
  title =	{{K4-free Graphs as a Free Algebra}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{76:1--76:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.76},
  URN =		{urn:nbn:de:0030-drops-80883},
  doi =		{10.4230/LIPIcs.MFCS.2017.76},
  annote =	{Keywords: Universal Algebra, Graph theory, Axiomatisation, Tree decompositions, Graph minors}
}

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K4-free Graphs as a Free Algebra

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