Robert Hickingbotham, Powers of planar graphs, product structure, and blocking partitions

Graph product structure theory describes complex graphs in terms of products of simpler graphs. In this talk, I will introduce this subject and talk about some of my recent results in this area. The focus of my talk will be on a new tool in graph product structure theory called `blocking partitions.’ I’ll show how this tool can be used to prove stronger product structure theorems for powers of planar graphs as well as $k$-planar graphs, resolving open problems of Dujmović, Morin and Wood, and Ossona de Mendez.