Dankelmann–Oellermann–Swart conjecture on average Steiner distance

Let $G$ be a connected graph of order $n\geq k$, and let $\mu(G)$ denote its average distance and $\mu_k(G)$ its average Steiner $k$-distance. Dankelmann–Oellermann–Swart conjecture. For $3\leq k\leq n$,

$$\mu_k(G)\geq 3\frac{k-1}{k+1}\mu(G).$$

Equivalently, the smallest ratio $\mu_k(G)/\mu(G)$ is conjectured to be attained by the path. The source describes the corresponding lower-bound problem as open.