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#### Partitions and orientations of the Rado graph

We classify the countably infinite oriented graphs which, for
every

partition of their vertex set into two parts, induce an isomorphic
copy of

themselves on at least one of the parts. These graphs are the
edgeless graph,

the random tournament, the transitive tournaments of order

type~$\omega^\alpha$, and two orientations of the Rado graph:
the random

oriented graph, and a newly found random acyclic oriented graph.

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