Treewidth of Cartesian Products of Highly Connected Graphs

TL;DR

This paper establishes a new lower bound on the treewidth of Cartesian products of highly connected graphs, generalizing known results for planar grid graphs and providing asymptotic tightness for large graphs.

Contribution

It proves a general lower bound on the treewidth of Cartesian products of highly connected graphs, extending previous results for specific graph classes.

Findings

Lower bound on treewidth for Cartesian products of k-connected graphs

Asymptotic tightness of the bound for large n

Generalization of planar grid graph results

Abstract

The following theorem is proved: For all $k$-connected graphs $G$ and $H$ each with at least $n$ vertices, the treewidth of the cartesian product of $G$ and $H$ is at least $k(n -2k+2)-1$. For $n\gg k$ this lower bound is asymptotically tight for particular graphs $G$ and $H$. This theorem generalises a well known result about the treewidth of planar grid graphs.