The cyclic difference rainbow embedding conjecture

Let $T$ be a tree with $n$ edges. Let $A$ and $B$ be two copies of $\mathbb{Z}_n$, and form the complete bipartite graph between them by colouring each edge $(a,b)\in A\times B$ with $b-a\in\mathbb{Z}_n$. A copy is rainbow if all its edge colours are distinct.

Cyclic difference rainbow embedding conjecture. The resulting edge-coloured bipartite graph contains a rainbow embedding of $T$.

Such an embedding would yield the Graham–Häggkvist decomposition by cyclic translations. The paper expects bounded-degree cases to follow from its methods, but the general conjecture remains open.