Abstract
In this paper we study the distance Ramsey number RD(s,t,d). The distance Ramsey numberRD(s,t,d) is the minimum number n such that for any graph G on n vertices, either G contains an induced s-vertex subgraph isomorphic to a distance graph in Rd or Ḡ contains an induced t-vertex subgraph isomorphic to the distance graph in Rd. 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]⌉).
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