LIPIcs.IPEC.2023.7.pdf
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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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Part of:
Volume:
18th International Symposium on Parameterized and Exact Computation (IPEC 2023)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Symposium on Parameterized and Exact Computation (IPEC) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2023-12-13
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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.
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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
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.
Subject Classification
ACM Subject Classification
- Theory of computation → Problems, reductions and completeness
Keywords
- Treewidth
- cubic graphs
- degree
- NP-completeness
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References
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