Trotignon's string-graph or biclique-induced-minor conjecture

A hereditary class is a graph class closed under induced subgraphs. A string graph is an intersection graph of curves in the plane, and $K_{\ell,\ell}$ is the complete bipartite graph with $\ell$ vertices in each part. Trotignon's conjecture. Every hereditary class of unbounded treewidth contains a subclass of string graphs of unbounded treewidth or a $K_{\ell,\ell}$ induced minor for every $\ell$. The conjecture is refuted in the paper using hereditary classes of unbounded treewidth that contain neither an unbounded-treewidth subclass of string graphs nor arbitrarily large bicliques as induced minors.