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A relational structure R is rainbow Ramsey if for every finite induced substructure C of R and every colouring of the copies of C with countably many colours, such that each colour is used at most k times for a fixed k, there exists a copy R^∗ of R so that the copies of C in R^∗ use each colour at most once. We show that certain ultrahomogenous binary relational structures, for example the Rado graph, are rainbow Ramsey. Via compactness this then implies that for all finite graphs B and C and karXiv:1411.6678v1 fatcat:2hast4l7uvfgxfglr2qu7qc7f4