Constantine's multicoloured tree parallelism conjecture

Let $K_n$ be a complete graph and let a $1$-factorization be an edge-colouring whose colour classes form a decomposition of $K_n$ into perfect matchings. A subgraph is rainbow if all its edges have distinct colours. A multicoloured tree parallelism (MTP) is a decomposition of an edge-coloured $K_n$ into isomorphic rainbow spanning trees. Constantine's conjecture. For all $n>4$, any $1$-factorization of $K_n$ admits a decomposition into isomorphic rainbow spanning trees. This strengthens the Brualdi–Hollingsworth conjecture by requiring all trees in the decomposition to be isomorphic. The source reports only weak asymptotic results before the paper; its main theorem proves the conjecture for sufficiently large $n$.