eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-08-27
60:1
60:15
10.4230/LIPIcs.MFCS.2018.60
article
Treewidth-Two Graphs as a Free Algebra
Doczkal, Christian
1
Pous, Damien
1
Univ Lyon, CNRS, ENS de Lyon, UCB Lyon 1, LIP, France
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol117-mfcs2018/LIPIcs.MFCS.2018.60/LIPIcs.MFCS.2018.60.pdf
Treewidth
Universal Algebra
Rewriting