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arXiv · 2001.08860

Notes on Graph Product Structure Theory

Zdeněk Dvořák·Tony Huynh·Gwenaël Joret·Chun-Hung Liu·David R. Wood
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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.

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Zdeněk Dvořák, Tony Huynh, Gwenaël Joret, Chun-Hung Liu, David R. Wood. 2020-07-02. Notes on Graph Product Structure Theory. https://doi.org/10.1007/978-3-030-62497-2_32

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