Geodesic
On the computational complexity of (O,P)-partition problems
Discussiones Mathematicae. Graph Theory, Tome 17 (1997) no. 2, pp. 253-258.

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We prove that for any additive hereditary property P > O, it is NP-hard to decide if a given graph G allows a vertex partition V(G) = A∪B such that G[A] ∈ (i.e., A is independent) and G[B] ∈ P.
Keywords: computational complexity, graph properties, partition problems 
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Kratochvíl, Jan; Schiermeyer, Ingo. On the computational complexity of (O,P)-partition problems. Discussiones Mathematicae. Graph Theory, Tome 17 (1997) no. 2, pp. 253-258. http://geodesic.mathdoc.fr/item/DMGT_1997_17_2_a3/

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[2] J. Bucko, M. Frick, P. Mihok and R. Vasky, Uniquely partitionable graphs, Discussiones Mathematicae Graph Theory 17 (1997) 103-113.

[3] P. Mihók, G. Semanišin, Additive hereditary properties are uniquely factorizable, Czecho-Slovak Conference on Combinatorics and Graph Theory, Chudenice, 1997.