Treewidth Is NP-Complete on Cubic Graphs

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

doi:10.4230/LIPIcs.IPEC.2023.7

Abstract

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.

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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) https://doi.org/10.4230/LIPIcs.IPEC.2023.7

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

Funding

Dušan Knop and Ondřej Suchý: Dušan Knop and Ondřej Suchý acknowledge the support of the Czech Science Foundation Grant No. 22-19557S.

Milanič, Martin: Martin Milanič acknowledges the support of the Slovenian Research and Innovation Agency (I0-0035, research program P1-0285 and research projects N1-0102, N1-0160, J1-3001, J1-3002, J1-3003, J1-4008, and J1-4084) and the research program CogniCom (0013103) at the University of Primorska.
Ordyniak, Sebastian: Sebastian Ordyniak acknowledges support by the Engineering and Physical Sciences Research Council (EPSRC, project EP/V00252X/1).

Acknowledgements

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

References

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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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