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Uniquely partitionable planar graphs with respect to properties having a forbidden tree
Discussiones Mathematicae. Graph Theory, Tome 19 (1999) no. 1, pp. 71-78 Cet article a éte moissonné depuis la source Library of Science

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Let ₁, ₂ be graph properties. A vertex (₁,₂)-partition of a graph G is a partition V₁,V₂ of V(G) such that for i = 1,2 the induced subgraph G[V_i] has the property _i. A property ℜ = ₁∘₂ is defined to be the set of all graphs having a vertex (₁,₂)-partition. A graph G ∈ ₁∘₂ is said to be uniquely (₁,₂)-partitionable if G has exactly one vertex (₁,₂)-partition. In this note, we show the existence of uniquely partitionable planar graphs with respect to hereditary additive properties having a forbidden tree.
Keywords: uniquely partitionable planar graphs, forbidden graphs 
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Bucko, Jozef; Ivančo, Jaroslav. Uniquely partitionable planar graphs with respect to properties having a forbidden tree. Discussiones Mathematicae. Graph Theory, Tome 19 (1999) no. 1, pp. 71-78. http://geodesic.mathdoc.fr/item/DMGT_1999_19_1_a5/

[1] J. Bucko, M. Frick, P. Mihók and R. Vasky, Uniquely partitionable graphs, Discuss. Math. Graph Theory 17 (1997) 103-114, doi: 10.7151/dmgt.1043.

[2] J. Bucko, P. Mihók and M. Voigt, Uniquely partitionable planar graphs, Discrete Math. 191 (1998) 149-158, doi: 10.1016/S0012-365X(98)00102-2.

[3] M. Borowiecki, J. Bucko, P. Mihók, Z. Tuza and M. Voigt, Remarks on the existence of uniquely partitionable planar graphs, 13. Workshop on Discrete Optimization, Burg, abstract, 1998.

[4] P. Mihók, Additive hereditary properties and uniquely partitionable graphs, in: M. Borowiecki and Z. Skupień, eds., Graphs, hypergraphs and matroids (Zielona Góra, 1985) 49-58.