Equality of the Helly and Radon numbers for connected graphs under $\Delta$-convexity

Let $G$ be a non-trivial connected graph. Write $h_\Delta(G)$ for its Helly number and $r_\Delta(G)$ for its Radon number with respect to $\Delta$-convexity.

Helly–Radon equality conjecture.

$$h_\Delta(G)=r_\Delta(G).$$

The conjecture proposes that, unlike in most familiar convexities on discrete structures, the Helly and Radon numbers coincide for every non-trivial connected graph under $\Delta$-convexity. The equality is established in the paper for chordal graphs, and the authors report it for all small graphs examined, but it remains open in general.