Treewidth is NP-Complete on Cubic Graphs (and related results)
Hans L. Bodlaender, \'Edouard Bonnet, Lars Jaffke, Du\v{s}an Knop,, Paloma T. Lima, Martin Milani\v{c}, Sebastian Ordyniak, Sukanya Pandey and, Ond\v{r}ej Such\'y
TL;DR
This paper provides a simple proof that computing treewidth is NP-complete, extending the complexity results to co-bipartite and cubic graphs, thus broadening the understanding of its computational difficulty.
Contribution
The paper offers a simplified proof of NP-completeness for Treewidth and establishes NP-completeness on cubic graphs, improving previous results on bounded-degree graphs.
Findings
NP-completeness of Treewidth on co-bipartite graphs
NP-completeness of Treewidth on cubic graphs
Simplified proof technique for NP-completeness
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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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Graph theory and applications