Treewidth is NP-Complete on Cubic Graphs (and related results)

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

arXiv · 2301.10031

Treewidth is NP-Complete on Cubic Graphs (and related results)

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

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Abstract

In this paper, we give a very simple proof that Treewidth is NP-complete; this proof also shows NP-completeness on the class of co-bipartite graphs. We then improve the result by Bodlaender and Thilikos from 1997 that Treewidth is NP-complete on graphs with maximum degree at most 9, by showing that Treewidth is NP-complete on cubic graphs.

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Hans L. Bodlaender, Édouard Bonnet, Lars Jaffke, Dušan Knop, Paloma T. Lima, Martin Milanič, Sebastian Ordyniak, Sukanya Pandey, Ondřej Suchý. 2023-01-24. Treewidth is NP-Complete on Cubic Graphs (and related results). https://arxiv.org/abs/2301.10031

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