License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2017.76
URN: urn:nbn:de:0030-drops-80883
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8088/
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Cosme Llópez, Enric ; Pous, Damien

K4-free Graphs as a Free Algebra

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LIPIcs-MFCS-2017-76.pdf (0.5 MB)

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.

BibTeX - Entry

@InProceedings{cosmellpez_et_al:LIPIcs:2017:8088,
  author =	{Enric Cosme Ll{\'o}pez and Damien Pous},
  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 =	{Kim G. Larsen and Hans L. Bodlaender and Jean-Francois Raskin},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8088},
  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}
}

Keywords: Universal Algebra, Graph theory, Axiomatisation, Tree decompositions, Graph minors
Collection: 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)
Issue Date: 2017
Date of publication: 01.12.2017

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