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Journal Articles Transactions of the American Mathematical Society Year : 2007

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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Dates and versions

lirmm-00153515 , version 1 (14-12-2007)

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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, 2007, 359, pp.2395-2405. ⟨10.1090/S0002-9947-06-04086-4⟩. ⟨lirmm-00153515⟩
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