Equivalent Rainbow Arborescence Conjecture for at least $n-1$ colors

Let $G$ be a digraph on a vertex set $V$ of size $n \ge 2$, formed as the disjoint union of $k$ spanning arborescences $A_1,\ldots,A_k$. A subgraph $B$ is rainbow if $|B \cap A_i| \le 1$ for every color $i$.

Equivalent Rainbow Arborescence Conjecture. If $k \ge n-1$, then the disjoint union $G$ of $k$ spanning arborescences has a rainbow spanning arborescence $B$.

The paper states that this formulation is equivalent to Yokoi's conjecture and may be easier to use when $k \ne n-1$. It remains open.