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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2018.60
URN: urn:nbn:de:0030-drops-96429
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9642/
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Doczkal, Christian ; Pous, Damien

Treewidth-Two Graphs as a Free Algebra

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LIPIcs-MFCS-2018-60.pdf (0.4 MB)


Abstract

We give a new and elementary proof that the graphs of treewidth at most two can be seen as a free algebra. This result was originally established through an elaborate analysis of the structure of K_4-free graphs, ultimately reproving the well-known fact that the graphs of treewidth at most two are precisely those excluding K_4 as a minor. Our new proof is based on a confluent and terminating rewriting system for term-labeled graphs and does not involve graph minors anymore. The new strategy is simpler and robust in the sense that it can be adapted to subclasses of treewidth-two graphs, e.g., graphs without self-loops.

BibTeX - Entry

@InProceedings{doczkal_et_al:LIPIcs:2018:9642,
  author =	{Christian Doczkal and Damien Pous},
  title =	{{Treewidth-Two Graphs as a Free Algebra}},
  booktitle =	{43rd International Symposium on Mathematical Foundations  of Computer Science (MFCS 2018)},
  pages =	{60:1--60:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Igor Potapov and Paul Spirakis and James Worrell},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9642},
  URN =		{urn:nbn:de:0030-drops-96429},
  doi =		{10.4230/LIPIcs.MFCS.2018.60},
  annote =	{Keywords: Treewidth, Universal Algebra, Rewriting}
}

Keywords: Treewidth, Universal Algebra, Rewriting
Seminar: 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)
Issue Date: 2018
Date of publication: 20.08.2018


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