The Graham–Häggkvist tree decomposition conjecture

Let $T$ be a tree with $n$ edges, and let $K_{n,n}$ be the balanced complete bipartite graph with $n$ vertices in each part.

Graham–Häggkvist conjecture. The edge set of $K_{n,n}$ can be decomposed into copies of every $n$-edge tree $T$.

This is the bipartite analogue of the tree-decomposition conjecture associated with Ringel. The source states that it remains open, although the paper discusses rainbow embedding approaches.