NP-completeness of coloring finite distance graphs

Let $D$ be a finite set of positive integers, and let $\chi(D)$ denote the chromatic number of the distance graph with distance set $D$. For a fixed integer $k\ge3$, consider the decision problem of determining whether $\chi(D)\le k$. NP-completeness conjecture. Determining whether $\chi(D)\le k$ for finite sets $D$ is NP-complete. This conjecture extends the known NP-completeness of deciding whether the chromatic number of a finite graph is at most $k$; the paper notes that an algorithm exists for computing $\chi(D)$ when $D$ is finite, but leaves the efficiency of that algorithm unresolved.