5 problems

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

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

Rainbow tree conjecture. For every tree $T$ on $d$ vertices, every properly coloured $d$-regular graph $G$ contains a rainbow copy of $T$.

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

The harmonious labelling conjecture. For every $n$-edge tree $T$, there exists a labelling $\phi\colon V(T)\to \mathbb{Z}_n$ such that the edge sums $\phi(x)+\phi(y)$ are all disti…