Abstract
A graphG is uniquelyn-cocolourable if (its cochromatic number)z(G) = n and alln-cocolourings ofG induce the same partition of its vertex set. We prove that there are infinitely many uniquelyn-cocolourable graphs and that the numbers of complete and empty colour classes can be prescribed. It is also shown that everyn-cocolourable graph is an induced subgraph of a uniquelyn-cocolourable graph.
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