The substitution conjecture for dichromatically bounded digraph classes

A class of digraphs $\mathcal C$ is dichromatically bounded if its dichromatic number is bounded as a function of its clique number. The substitution conjecture. If a class of digraphs $\mathcal C$ is $\operatorname{\overrightarrow{\chi}}$-bounded, then so is its closure under substitution. The paper presents this as a future direction; it is not established for general digraphs.