Notes on Graph Product Structure Theory
Combinatorics
2021-02-18 v2 Computational Geometry
Discrete Mathematics
Abstract
It was recently proved that every planar graph is a subgraph of the strong product of a path and a graph with bounded treewidth. This paper surveys generalisations of this result for graphs on surfaces, minor-closed classes, various non-minor-closed classes, and graph classes with polynomial growth. We then explore how graph product structure might be applicable to more broadly defined graph classes. In particular, we characterise when a graph class defined by a cartesian or strong product has bounded or polynomial expansion. We then explore graph product structure theorems for various geometrically defined graph classes, and present several open problems.
Keywords
Cite
@article{arxiv.2001.08860,
title = {Notes on Graph Product Structure Theory},
author = {Zdeněk Dvořák and Tony Huynh and Gwenaël Joret and Chun-Hung Liu and David R. Wood},
journal= {arXiv preprint arXiv:2001.08860},
year = {2021}
}
Comments
19 pages, 0 figures