The structure of planar graphs

This talk is about the global structure of planar graphs and other more general graph classes. The starting point is the Lipton-Tarjan separator theorem, followed by Baker's decomposition of a planar graph into layers with bounded treewidth. I will then move onto layered treewidth, which is a more global version of Baker's decomposition. Layered treewidth is a precursor to the recent development of row treewidth, which has been the key to solving several open problems. Finally, I will describe generalisations for arbitrary minor-closed classes.