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Criteria for of the existence of uniquely partitionable graphs with respect to additive induced-hereditary properties

100%

Broere I., Bucko J., Mihók P.

Discussiones Mathematicae Graph Theory

2002

tom 22

nr 1

31-37

Let 𝓟₁,𝓟₂,...,𝓟ₙ be graph properties, a graph G is said to be uniquely (𝓟₁,𝓟₂, ...,𝓟ₙ)-partitionable if there is exactly one (unordered) partition {V₁,V₂,...,Vₙ} of V(G) such that $G[V_i] ∈ 𝓟_i$ for i = 1,2,...,n. We prove that for additive and induced-hereditary properties uniquely (𝓟₁,𝓟₂,...,𝓟ₙ)-partitionable graphs exist if and only if $𝓟_i$ and $𝓟_j$ are either coprime or equal irreducible properties of graphs for every i ≠ j, i,j ∈ {1,2,...,n}.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Broere I.

1 Bucko J.

1 Mihók P.

1 2002

Wyniki wyszukiwania

Criteria for of the existence of uniquely partitionable graphs with respect to additive induced-hereditary properties