Coloring of integer distance graphs

Abstract

An integer distance graph is a graph G( D) with the set of integers as vertex set and with an edge joining two vertices u and v if and only if | u − v ∈ D where D is a subset of the positive integers. We determine the chromatic number χ( D) of G( D) for some finite distance sets D such as sets of consecutive integers and special sets of cardinality 4.