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 has the property . 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1086,
author = {Jozef Bucko and Jaroslav Ivan\v co},
title = {Uniquely partitionable planar graphs with respect to properties having a forbidden tree},
journal = {Discussiones Mathematicae Graph Theory},
volume = {19},
year = {1999},
pages = {71-78},
zbl = {0944.05080},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1086}
}
Jozef Bucko; Jaroslav Ivančo. Uniquely partitionable planar graphs with respect to properties having a forbidden tree. Discussiones Mathematicae Graph Theory, Tome 19 (1999) pp. 71-78. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1086/
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