Treewidth-Two Graphs as a Free Algebra - Archive ouverte HAL Access content directly
Conference Papers Year : 2018

Treewidth-Two Graphs as a Free Algebra

Damien Pous


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 presented last year at MFCS and was proved through an elaborate analysis of the structure of K4-free graphs, ultimately reproving the well-known fact that the graphs of treewidth at most two are precisely those excluding K4 as a minor. Our new proof is based on a confluent and terminating rewriting system for treewidth-two 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. It could also be amenable to handle graphs of larger treewidth, where the excluded minors are typically unknown.
Fichier principal
Vignette du fichier
tw2fa.pdf (418.03 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-01780844 , version 1 (28-04-2018)
hal-01780844 , version 2 (12-09-2018)
hal-01780844 , version 3 (12-09-2018)



Christian Doczkal, Damien Pous. Treewidth-Two Graphs as a Free Algebra. Mathematical Foundations of Computer Science, Aug 2018, Liverpool, United Kingdom. ⟨10.4230/LIPIcs.MFCS.2018.60⟩. ⟨hal-01780844v2⟩
288 View
275 Download



Gmail Mastodon Facebook X LinkedIn More