The bunchy factor conjecture in terms of the maximal bunchy factor

Let $G$ be a strongly connected graph, and let $B(G)$ denote the unique $\leq_R$-maximal right-resolving bunchy factor of $G$. Write $H\leq_S G$ when there is a synchronizing right resolver from $G$ to $H$.

Bunchy factor conjecture. For every strongly connected graph $G$,

$$B(G)\leq_S G.$$

This is presented as an equivalent formulation of the assertion that every strongly connected graph has a bunchy synchronizing factor. The source reports supporting results for bi-resolving graphs and computational evidence, but the general conjecture remains unresolved in the supplied text.