New bounds for the distance Ramsey number

In this paper we study the distance Ramsey number RD(s,t,d). The distance Ramsey number  RD(s,t,d) is the minimum number nn such that for any graph GG on nn vertices, either GG contains an induced ss-vertex subgraph isomorphic to a distance graph in RdRd or Ḡ contains an induced tt-vertex subgraph isomorphic to the distance graph in RdRd. We obtain the upper and lower bounds on RD(s,s,d), which are similar to the bounds for the classical Ramsey number R(⌈s[d/2]⌉,⌈s[d/2]⌉).