@inbook{daba7d5cf38d40c2a3334b4d2acdd940,

title = "Notes on Graph Product Structure Theory",

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.",

author = "Zden{\v e}k Dvo{\v r}{\'a}k and Tony Huynh and Gwena{\"e}l Joret and Chunhung Liu and Wood, {David R}",

year = "2021",

doi = "10.1007/978-3-030-62497-2_32",

language = "English",

isbn = "9783030624965",

volume = "4",

series = "MATRIX Book Series",

publisher = "Springer",

number = "1",

pages = "513--533",

editor = "Wood, {David R} and {de Gier}, Jan and Praeger, {Cheryl E} and Terence Tao",

booktitle = "2019-20 MATRIX Annals",

edition = "1",

}