Aboulker–Aubian–Charbit–Lopes conjecture on forest backedge graphs

Let $T$ be a tournament and suppose that one of its backedge graphs is a forest. For a tournament, let its clique number mean the minimum clique number of a backedge graph over all vertex orderings, and let its dichromatic number be the minimum number of acyclic vertex classes in a partition. Aboulker–Aubian–Charbit–Lopes conjecture. For every $k\in\mathbb N$, the class of tournaments not containing $T$ as a subtournament and having clique number at most $k$ has bounded dichromatic number. The paper announces a counterexample and proves that this conjecture is false.