Nordhaus-Gaddum for Treewidth

TL;DR

This paper establishes a tight bound relating the treewidth of any graph to that of its complement, showing their sum is at least the number of vertices minus two.

Contribution

It proves a tight lower bound on the sum of treewidths of a graph and its complement, a novel theoretical result in graph theory.

Findings

The sum of treewidths of a graph and its complement is at least n-2.

The bound is proven to be tight, meaning it cannot be improved.

The result applies to all graphs with n vertices.

Abstract

We prove that for every graph $G$ with $n$ vertices, the treewidth of $G$ plus the treewidth of the complement of $G$ is at least $n-2$. This bound is tight.