Rainbow Hamilton cycle conjecture for bounded edge-colourings of Dirac graphs

Let $G$ be a Dirac graph on $n$ vertices, meaning a graph with minimum degree at least $n/2$, and let its edge-colouring be proper if every pair of incident edges receives different colours. The colouring is $n/8$-bounded if each colour is assigned to at most $n/8$ edges. A Hamilton cycle is rainbow if all its edges receive distinct colours. Rainbow Hamilton cycle conjecture. There exists a rainbow Hamilton cycle in any proper $n/8$-bounded edge-colouring of a Dirac graph on $n$ vertices. The paper proves near-rainbow results and shows that the constant $1/8$ is best possible up to lower-order terms, leaving the exact $n/8$-bounded assertion open.