Dirac subgraphs of powers of cycles are Hamiltonian

We show that, for every $\varepsilon>0$ and all sufficiently large $k$, any spanning subgraph of the $k$th power of a cycle with minimum degree at least $(1+\varepsilon)k$ contains a Hamilton cycle. This asymptotically settles a conjecture of Espuny D\'iaz, Lichev, and Wesolek.