Kevin Hendrey, Product Structure of Graph Classes with Bounded Treewidth

The strong product $G\boxtimes H$ of graphs $G$ and $H$ is the graph on the cartesian product $V(G)\times V(H)$ such that vertices $(v,w)$ and $(x,y)$ are adjacent if and only if $\max\{d_G(v,x),d_H(w,y)\}=1$. Graph product structure theory aims to describe complicated graphs in terms of subgraphs of strong products of simpler graphs. This area of research was initiated by Dujmović, Joret, Micek, Morin, Ueckerdt and Wood, who showed that every planar graph is a subgraph of the strong product of a $H\boxtimes P\boxtimes K_3$ for some path $P$ and some graph $H$ of treewidth at most $3$. In this talk, I will discuss the product structure of various graph classes of bounded treewidth. As an example, we show that there is a function $f:\mathbb{N}\rightarrow \mathbb{N}$ such that every planar graph of treewidth at most $k$ is a subgraph of $H\boxtimes K_{f(k)}$ for some graph $H$ of treewidth at most $3$.

This is based on joint work with Campbell, Clinch, Distel, Gollin, Hickingbotham, Huynh, Illingworth, Tamitegama, Tan and Wood.