The oriented rainbow tree conjecture

Let $D$ be a digraph in which every vertex has $d$ incoming and $d$ outgoing edges, with no loops or parallel edges; both $a\to b$ and $b\to a$ may occur. It is properly coloured when the incoming edges at each vertex have distinct colours and the outgoing edges at each vertex have distinct colours. Let $T$ be an oriented tree with $d-1$ edges; a copy is rainbow when its edges have distinct colours.

Oriented rainbow tree conjecture. Every $d$-regular properly coloured digraph $D$ contains a rainbow copy of every oriented tree $T$ on $d-1$ edges.

This strictly generalises the undirected regular-graph rainbow tree conjecture and implies several longstanding rainbow and rearrangement problems. The source explicitly describes the associated consequences as open.