Chudnovsky–Scott–Seymour's Burling-control conjecture

A graph class is Burling-controlled when its chromatic complexity is controlled by the Burling graphs, as defined in the source. An induced subdivision of a graph $F$ is a subdivision appearing as an induced subgraph. Chudnovsky–Scott–Seymour's Burling-control conjecture. For every graph $F$, the class of graphs excluding induced subdivisions of $F$ is Burling-controlled. This is proposed as a resuscitated form of Scott's refuted conjecture: Burling's construction is the only known obstruction to Scott's statement, and the conjecture remains open.