Grid Minors and Products
Combinatorics
2025-05-12 v3 Discrete Mathematics
Abstract
Motivated by recent developments regarding the product structure of planar graphs, we study relationships between treewidth, grid minors, and graph products. We show that the Cartesian product of any two connected -vertex graphs contains an grid minor. This result is tight: The lexicographic product (which includes the Cartesian product as a subgraph) of a star and any -vertex tree has no grid minor.
Cite
@article{arxiv.2402.14181,
title = {Grid Minors and Products},
author = {Vida Dujmović and Pat Morin and David R. Wood and David Worley},
journal= {arXiv preprint arXiv:2402.14181},
year = {2025}
}