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Uniquely partitionable planar graphs with respect to properties having a forbidden tree

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Bucko J., Ivančo J.

Discussiones Mathematicae Graph Theory

1999

tom 19

nr 1

71-78

Let 𝓟₁, 𝓟₂ be graph properties. A vertex (𝓟₁,𝓟₂)-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 $𝓟_i$. A property ℜ = 𝓟₁∘𝓟₂ is defined to be the set of all graphs having a vertex (𝓟₁,𝓟₂)-partition. A graph G ∈ 𝓟₁∘𝓟₂ is said to be uniquely (𝓟₁,𝓟₂)-partitionable if G has exactly one vertex (𝓟₁,𝓟₂)-partition. In this note, we show the existence of uniquely partitionable planar graphs with respect to hereditary additive properties having a forbidden tree.

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1 Discussiones Mathematicae Graph Theory

1 Bucko J.

1 Ivančo J.

1 1999

Wyniki wyszukiwania

Uniquely partitionable planar graphs with respect to properties having a forbidden tree