The forest and bipartite-complement boundary conjecture for bipartite graph classes

Let $T$ be a tree, let $T^b$ denote the bipartite representation of $T$, and let $\overline{T^b}$ denote its bipartite complement. A class is at most factorial when its speed is bounded above by a factorial function.

Forest boundary conjecture. For any tree $T$, the class of $\{T,\overline{T^b}\}$-free bipartite graphs is at most factorial.

In the terminology of boundary classes, this is equivalent to asserting that the class of forests and the class of their bipartite complements are the only boundary classes among hereditary properties of bipartite graphs. The conjecture is proposed as the missing step toward characterizing factorial classes defined by finitely many forbidden induced bipartite subgraphs, and remains open in the source.