Hahn's rainbow Hamilton path conjecture

Let $K_n$ be the complete graph on $n$ vertices. An edge-colouring is $k$-bounded if no colour appears on more than $k$ edges. A subgraph is rainbow if no two of its edges have the same colour. Hahn's conjecture. Any $(n/2)$-bounded colouring of $E(K_n)$ contains a rainbow Hamilton path. The conjecture was disproved by Maamoun and Meyniel, who showed that it fails even for proper colourings of $K_{2^t}$ when $t\geq 2$.