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.

翻译：本文给出了树宽问题是NP完全的一个非常简单的证明；该证明还表明树宽在共二部图类上是NP完全的。随后，我们改进了Bodlaender与Thilikos于1997年提出的结果（树宽在最大度不超过9的图上NP完全），通过证明树宽在三次图上也是NP完全的。