The bounded-twin-width subclass conjecture for hereditary classes

A hereditary class is a graph class closed under induced subgraphs, and twin-width is the graph parameter measuring the minimum contraction complexity under sequences of vertex identifications. Bounded-twin-width conjecture. Every hereditary class of unbounded treewidth admits a subclass of unbounded treewidth and bounded twin-width. The paper notes that its constructions do not refute this conjecture, since bounded twin-width is not treewidth-hereditary; the conjecture remains open.