Hamilton decomposition conjecture for regular tripartite tournaments

A tripartite tournament is an orientation of a complete tripartite graph. It is regular when all vertex classes have equal size and every vertex has equal indegree and outdegree. A Hamilton decomposition is a decomposition of its arcs into directed Hamilton cycles.

Tripartite tournament conjecture. Every regular tripartite tournament has a Hamilton decomposition.

The paper proves the corresponding result for regular $k$-partite tournaments with $k\ge 4$ and explicitly conjectures that it extends to all $k\ge 2$. The tripartite case is therefore the first unresolved case beyond the proven range.