Packing chromatic number of distance graphs

In this paper we focus on distance graphs with D={1,t}. We improve some results of Togni who initiated the study. It is shown that χρ(G(Z,D))≤35 for sufficiently large odd t and χρ(G(Z,D))≤56 for sufficiently large even t. We also give a lower bound 12 for t≥9 and tighten several gaps for χρ(G(Z,D)) with small t.