Harvey's minimum-degree conjecture on chords of longest cycles

Let $G$ be a graph on $n$ vertices, let $\delta(G)$ denote its minimum degree, and let a cycle of maximum order mean a cycle containing the maximum possible number of vertices in $G$. Harvey's conjecture. If

$$\delta(G)\geq \sqrt{n},$$

then every cycle of maximum order in $G$ contains a chord.

The source attributes this conjecture to Harvey and does not state a resolution. The paper proves related results under large-circumference hypotheses, but the stated minimum-degree conjecture remains open on the supplied evidence.