Chord conjecture for longest cycles containing a linear forest

Let $G$ be a $k$-connected graph with $k\geq 2$, and let $F$ be a linear forest, meaning a graph whose components are paths, that is a subgraph of $G$ with $l$ edges and $t$ isolated vertices. Assume that

$$l+t\leq k-2.$$

A longest cycle passing through $F$ is a cycle containing $F$ with maximum length among all cycles of $G$ that contain $F$. Wu--Zhang's conjecture. Every longest cycle of $G$ passing through $F$ has a chord.

The connectivity assumption ensures that a cycle containing $F$ exists. The paper proves the conjecture for several cases involving a linear forest with at most one edge and sufficiently large circumference, while the full statement remains open on the supplied evidence.