Clément Rambaud

Product structure of graphs excluding a topological minor

We prove that, for all positive integers $h$ and $t$ and every graph $X$ with $\mathrm{td}(X) \leq h$, there exists a positive integer $c(X,t)$ such that every graph $G$ with $\mathrm{tw}(G)<t$ that excludes $X$ as a topological minor is isomorphic to a subgraph of $H \boxtimes K_{c(X,t)}$ for some graph $H$ with $\mat...