Colouring of Distance Graphs

Let \(D\) be a set of natural numbers. The distance graph \(G(D)\) has the integers as vertex set and two vertices \(u\) and \(v\) are adjacent if and only if \(|u – v| \in D\).
In the eighties, there have been some results concerning the chromatic number \(\chi(D)\) of these graphs, especially by Eggleton, Erdős, Skilton, and Walther. Most of these investigations are concentrated on distance graphs where the distance set \(D\) is a subset of primes.
This paper deals with the chromatic number of distance graphs of \(3\)-element distance sets without further restrictions for the elements of \(D\).