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Partitions and orientations of the Rado graph

Abstract : 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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Submitted on : Friday, December 14, 2007 - 1:42:45 PM
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Reinhard Diestel, Imre Leader, Alex Scott, Stéphan Thomassé. Partitions and orientations of the Rado graph. Transactions of the American Mathematical Society, American Mathematical Society, 2007, 359, pp.2395-2405. ⟨10.1090/S0002-9947-06-04086-4⟩. ⟨lirmm-00153515⟩



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