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The \\textit{distance Ramsey number} $R_{{\\it D}}(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 $ \\Real^d $ or $ \\bar {G} $ contains an induced $ t $-vertex subgraph isomorphic to the distance graph in $ \\Real^d $. 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