Kühn–Lapinskas–Osthus exact Hamilton-cycle packing conjecture

Let $G$ be a graph on $n$ vertices with minimum degree $\delta(G)\ge n/2$. Kühn–Lapinskas–Osthus conjecture. The graph $G$ contains $\operatorname{reg}_{\operatorname{even}}(G)/2$ edge-disjoint Hamilton cycles. The conjecture is proved for sufficiently high minimum degree and has an approximate version above $(1+\varepsilon)n/2$, but remains open in general.