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.2018.60
URN: urn:nbn:de:0030-drops-96429
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9642/
Doczkal, Christian ;
Pous, Damien
Treewidth-Two Graphs as a Free Algebra
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}
}
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Keywords: |
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Treewidth, Universal Algebra, Rewriting |
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Collection: |
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43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018) |
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Issue Date: |
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2018 |
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Date of publication: |
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27.08.2018 |
