Treewidth Is NP-Complete on Cubic Graphs

Authors Hans L. Bodlaender , Édouard Bonnet , Lars Jaffke , Dušan Knop , Paloma T. Lima , Martin Milanič , Sebastian Ordyniak , Sukanya Pandey , Ondřej Suchý

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Author Details

Hans L. Bodlaender
  • Utrecht University, The Netherlands
Édouard Bonnet
  • LIP, ENS Lyon, France
Lars Jaffke
  • University of Bergen, Norway
Dušan Knop
  • Czech Technical University in Prague, Czech Republic
Paloma T. Lima
  • IT University of Copenhagen, Denmark
Martin Milanič
  • FAMNIT and IAM, University of Primorska, Koper, Slovenia
Sebastian Ordyniak
  • University of Leeds, UK
Sukanya Pandey
  • Utrecht University, The Netherlands
Ondřej Suchý
  • Czech Technical University in Prague, Czech Republic


This research was conducted in the Lorentz Center, Leiden, the Netherlands, during the workshop Graph Decompositions: Small Width, Big Challenges, October 24-28, 2022.

Cite AsGet BibTex

Hans L. Bodlaender, Édouard Bonnet, Lars Jaffke, Dušan Knop, Paloma T. Lima, Martin Milanič, Sebastian Ordyniak, Sukanya Pandey, and Ondřej Suchý. Treewidth Is NP-Complete on Cubic Graphs. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 7:1-7:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


In this paper, we show that Treewidth is NP-complete for cubic graphs, thereby improving the result by Bodlaender and Thilikos from 1997 that Treewidth is NP-complete on graphs with maximum degree at most 9. We add a new and simpler proof of the NP-completeness of treewidth, and show that Treewidth remains NP-complete on subcubic induced subgraphs of the infinite 3-dimensional grid.

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
  • Treewidth
  • cubic graphs
  • degree
  • NP-completeness


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