Fixed-dimensional hardness conjecture for MAX-EMST-ratio

For a point set in Euclidean space, the $k$-MAX-EMST-ratio problem restricts the input to $k$ dimensions. Fixed-dimensional hardness conjecture. The $k$-MAX-EMST-ratio problem for $k\in\{2,3\}$ is NP-hard.

The unrestricted MAX-EMST-ratio problem is established to be NP-hard, while hardness in the specific practical dimensions $2$ and $3$ remains conjectural.