Behsaz–Hatami–Mahmoodian's minimum vertex-cover conjecture for generalized Petersen graphs

Let $P(n,k)$ be the generalized Petersen graph, and let $\beta(P(n,k))$ denote the size of a minimum vertex cover. Behsaz–Hatami–Mahmoodian's conjecture. For all $n$ and $k$,

$$\beta(P(n,k))\leq n+\left\lceil\frac{n}{5}\right\rceil.$$

Since the paper gives no resolution of this conjecture, its status remains open.