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Factorizations of properties of graphs

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Broere I., Teboho Moagi S., Mihók P., Vasky R.

Discussiones Mathematicae Graph Theory

1999

tom 19

nr 2

167-174

A property of graphs is any isomorphism closed class of simple graphs. For given properties of graphs 𝓟₁,𝓟₂,...,𝓟ₙ a vertex (𝓟₁, 𝓟₂, ...,𝓟ₙ)-partition of a graph G is a partition {V₁,V₂,...,Vₙ} of V(G) such that for each i = 1,2,...,n the induced subgraph $G[V_i]$ has property $𝓟_i$. The class of all graphs having a vertex (𝓟₁, 𝓟₂, ...,𝓟ₙ)-partition is denoted by 𝓟₁∘𝓟₂∘...∘𝓟ₙ. A property 𝓡 is said to be reducible with respect to a lattice of properties of graphs 𝕃 if there are n ≥ 2 properties 𝓟₁,𝓟₂,...,𝓟ₙ ∈ 𝕃 such that 𝓡 = 𝓟₁∘𝓟₂∘...∘𝓟ₙ; otherwise 𝓡 is irreducible in 𝕃. We study the structure of different lattices of properties of graphs and we prove that in these lattices every reducible property of graphs has a finite factorization into irreducible properties.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Broere I.

1 Mihók P.

1 Teboho Moagi S.

1 Vasky R.

1 1999

Wyniki wyszukiwania

Factorizations of properties of graphs