Seymour's conjecture on powers of Hamilton cycles

Let $G$ be a graph on $n$ vertices, and let the $k$th power of a Hamilton cycle be the graph obtained by joining every pair of vertices whose distance along the cycle is at most $k$. Let $\delta(G)$ denote the minimum degree of $G$.

Seymour's conjecture. For positive integers $n$ and $k$ with $n\geq k+1$ and $k\geq2$, if

$$\delta(G)\geq\frac{k}{k+1}n,$$

then $G$ contains the $k$th power of a Hamilton cycle.

This generalizes Pósa's conjecture and Dirac's theorem by prescribing a minimum-degree threshold for every power of a Hamilton cycle. The supplied text does not state whether it has been resolved.