Clarke–Hochberg–Hurlbert connectivity conjecture for graph pebbling

Let $d\ge 1$. For a finite graph $\mathbf{G}$, let its diameter be the maximum distance between two vertices, let its connectivity be the minimum number of vertices whose removal disconnects the graph, and call $\mathbf{G}$ Class $0$ when its pebbling number $f(\mathbf{G})$ equals its number of vertices. Clarke–Hochberg–Hurlbert conjecture. For each $d\ge 1$, there exists a least positive integer $k(d)$ such that every graph of diameter $d$ and connectivity at least $k(d)$ belongs to Class $0$. The conjecture concerns a threshold connectivity guaranteeing the Class $0$ pebbling property; the source indicates that Clarke, Hochberg and Hurlbert formulated it, while the surrounding text does not establish its resolution.