Geodesic
The order of uniquely partitionable graphs
Discussiones Mathematicae. Graph Theory, Tome 17 (1997) no. 1, pp. 115-125

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Let ₁,...,ₙ be properties of graphs. A (₁,...,ₙ)-partition of a graph G is a partition V₁,...,Vₙ of V(G) such that, for each i = 1,...,n, the subgraph of G induced by V_i has property _i. If a graph G has a unique (₁,...,ₙ)-partition we say it is uniquely (₁,...,ₙ)-partitionable. We establish best lower bounds for the order of uniquely (₁,...,ₙ)-partitionable graphs, for various choices of ₁,...,ₙ.
Keywords: hereditary property of graphs, uniquely partitionable graphs 
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Broere, Izak; Frick, Marietjie; Mihók, Peter. The order of uniquely partitionable graphs. Discussiones Mathematicae. Graph Theory, Tome 17 (1997) no. 1, pp. 115-125. http://geodesic.mathdoc.fr/item/DMGT_1997_17_1_a7/