Yokoi's Rainbow Arborescence Conjecture

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

Yokoi's Rainbow Arborescence Conjecture. If $G$ is the disjoint union of $n-1$ spanning arborescences $A_1, A_2, \dots, A_{n-1}$, then $G$ has a rainbow spanning arborescence $B$.

Since a spanning arborescence has $n-1$ arcs, such a $B$ uses every color exactly once. The paper reports verification in several cases, while the general conjecture remains open; testing existence with a fixed root is NP-complete.