# On infinite uniquely partitionable graphs and graph properties of finite character

Discussiones Mathematicae Graph Theory (2009)

- Volume: 29, Issue: 2, page 241-251
- ISSN: 2083-5892

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topJozef Bucko, and Peter Mihók. "On infinite uniquely partitionable graphs and graph properties of finite character." Discussiones Mathematicae Graph Theory 29.2 (2009): 241-251. <http://eudml.org/doc/270677>.

@article{JozefBucko2009,

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

author = {Jozef Bucko, Peter Mihók},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {graph property of finite character; reducibility; uniquely partitionable graphs; weakly universal graph},

language = {eng},

number = {2},

pages = {241-251},

title = {On infinite uniquely partitionable graphs and graph properties of finite character},

url = {http://eudml.org/doc/270677},

volume = {29},

year = {2009},

}

TY - JOUR

AU - Jozef Bucko

AU - Peter Mihók

TI - On infinite uniquely partitionable graphs and graph properties of finite character

JO - Discussiones Mathematicae Graph Theory

PY - 2009

VL - 29

IS - 2

SP - 241

EP - 251

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

LA - eng

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

UR - http://eudml.org/doc/270677

ER -

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