Ryser's conjecture on rainbow cycle packings

Let $\vec{K}_n$ be the complete directed graph with both directed edges between every pair of vertices and a loop at every vertex, properly edge-coloured with $n$ colours. A rainbow spanning subgraph is one whose edges have distinct colours.

Ryser's conjecture. If $n$ is odd, then $\vec{K}_n$ contains a rainbow spanning subgraph in which every vertex has in-degree and out-degree equal to one. Equivalently, $\vec{K}_n$ can be packed with directed cycles in a rainbow fashion.

This is a conjecture about rainbow cycle decompositions of properly coloured complete directed graphs. The paper presents it as a famous open problem and discusses related strengthening by prescribing cycle lengths.