The chromatic numbers of distance graphs Original Research Article

Suppose D is a subset of all positive integers L. The distance graph G(L,D) is the graph with vertex set L and two vertices x, y are adjacent if |x − y| ∈ D. This paper studies the chromatic number of G(L,D). We shall concentrate on the case that |D| = 3 and give a complete classification of those D = {a, b, c} for which b is a multiple of a and χ(G(L,D)) = 3.