Search Results

Documents authored by Humeau, Samuel


Document
Track B: Automata, Logic, Semantics, and Theory of Programming
A Finite Presentation of Graphs of Treewidth at Most Three

Authors: Amina Doumane, Samuel Humeau, and Damien Pous

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)


Abstract
We provide a finite equational presentation of graphs of treewidth at most three, solving an instance of an open problem by Courcelle and Engelfriet. We use a syntax generalising series-parallel expressions, denoting graphs with a small interface. We introduce appropriate notions of connectivity for such graphs (components, cutvertices, separation pairs). We use those concepts to analyse the structure of graphs of treewidth at most three, showing how they can be decomposed recursively, first canonically into connected parallel components, and then non-deterministically. The main difficulty consists in showing that all non-deterministic choices can be related using only finitely many equational axioms.

Cite as

Amina Doumane, Samuel Humeau, and Damien Pous. A Finite Presentation of Graphs of Treewidth at Most Three. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 135:1-135:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{doumane_et_al:LIPIcs.ICALP.2024.135,
  author =	{Doumane, Amina and Humeau, Samuel and Pous, Damien},
  title =	{{A Finite Presentation of Graphs of Treewidth at Most Three}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{135:1--135:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.135},
  URN =		{urn:nbn:de:0030-drops-202787},
  doi =		{10.4230/LIPIcs.ICALP.2024.135},
  annote =	{Keywords: Graphs, treewidth, connectedness, axiomatisation, series-parallel expressions}
}
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail