Integral distance graphs
Jer-Jeong Chen, Gerard J. Chang, Kuo‐Ching Huang · Journal of Graph Theory · 1997
Suppose D is a subset of all positive integers. The distance graph G(Z, D) with distance set D is the graph with vertex set Z, and two vertices x and y are adjacent if and only if |x − y| ≡ D. This paper studies the chromatic number χ(Z, D) of G(Z, D). In particular, we prove that χ(Z, D) ≤ |D| + 1 when |D| is finite. Exact values of χ(G, D) are also determined for some D with |D| = 3. © 1997 John Wiley & Sons, Inc. J Graph Theory 25: 287–294, 1997