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≫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.
@article{arxiv.1105.1586,
title = {Treewidth of Cartesian Products of Highly Connected Graphs},
author = {David R. Wood},
journal= {arXiv preprint arXiv:1105.1586},
year = {2013}
}