On infinite uniquely partitionable graphs and graph properties of finite character

• Autorzy: Jozef Bucko , Peter Mihók
• Języki publikacji: EN

Abstrakty

EN

A graph property is any nonempty isomorphism-closed class of simple (finite or infinite) graphs. A graph property 𝓟 is of finite character if a graph G has a property 𝓟 if and only if every finite induced subgraph of G has a property 𝓟. Let 𝓟₁,𝓟₂,...,𝓟ₙ be graph properties of finite character, a graph G is said to be (uniquely) (𝓟₁, 𝓟₂, ...,𝓟ₙ)-partitionable if there is an (exactly one) partition {V₁, V₂, ..., Vₙ} of V(G) such that $G[V_i] ∈ 𝓟_i$ for i = 1,2,...,n. Let us denote by ℜ = 𝓟₁ ∘ 𝓟₂ ∘ ... ∘ 𝓟ₙ the class of all (𝓟₁,𝓟₂,...,𝓟ₙ)-partitionable graphs. A property ℜ = 𝓟₁ ∘ 𝓟₂ ∘ ... ∘ 𝓟ₙ, n ≥ 2 is said to be reducible. We prove that any reducible additive graph property ℜ of finite character has a uniquely (𝓟₁, 𝓟₂, ...,𝓟ₙ)-partitionable countable generating graph. We also prove that for a reducible additive hereditary graph property ℜ of finite character there exists a weakly universal countable graph if and only if each property $𝓟_i$ has a weakly universal graph.

Słowa kluczowe

EN

graph property of finite character; reducibility; uniquely partitionable graphs; weakly universal graph

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs
• 05C75: Structural characterization of families of graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2009
• Tom: 29
• Numer: 2
• Strony: 241-251

Daty

wydano

2009

otrzymano

2007-12-31

poprawiono

2008-11-27

zaakceptowano

2008-12-01

Twórcy

autor

Jozef Bucko

• Department of Applied Mathematics, Faculty of Economics, Technical University, B. Nĕmcovej, 040 01 Košice, Slovak Republic

autor

Peter Mihók

• Department of Applied Mathematics, Faculty of Economics, Technical University, B. Nĕmcovej, 040 01 Košice, Slovak Republic
• Mathematical Institute, Slovak Academy of Science, Gresákova 6, 040 01 Košice, Slovak Republic

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1444