The Chang–Hsu–Rogers rainbow embedding conjecture

Let $G$ be an abelian group, and let $K_G$ be the complete graph on vertex set $G$, with each edge $xy$ coloured by $x+y$. A copy is rainbow when all its edge colours are distinct.

Chang–Hsu–Rogers conjecture. For every $n$-vertex tree $T$, the edge-coloured graph $K_{\mathbb{Z}_n}$ contains a rainbow copy of $T$.

This stronger rainbow-embedding formulation would imply the harmonious labelling conjecture. The paper confirms it for bounded-degree trees, while the general case remains open.