Conjecture (from prior work): NP-hardness of unit-ball contact graph recognition in arbitrary dimensions

Establish that, for every fixed dimension d ≥ 2, recognizing unit-ball contact graphs in ℝ^d is NP-hard.

Background

The authors survey earlier results on recognizing unit-ball contact graphs (marble graphs) and note NP-hardness for specific dimensions (e.g., d = 3, 4, 8, 24). They report that prior works conjectured NP-hardness in arbitrary dimensions, a broad statement still unresolved in the literature.