Factorizations of properties of graphs

Izak Broere, et al. "Factorizations of properties of graphs." Discussiones Mathematicae Graph Theory 19.2 (1999): 167-174. <http://eudml.org/doc/270424>.

@article{IzakBroere1999,
abstract = {A property of graphs is any isomorphism closed class of simple graphs. For given properties of graphs ₁,₂,...,ₙ a vertex (₁, ₂, ...,ₙ)-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 $_i$. The class of all graphs having a vertex (₁, ₂, ...,ₙ)-partition is denoted by ₁∘₂∘...∘ₙ. A property is said to be reducible with respect to a lattice of properties of graphs if there are n ≥ 2 properties ₁,₂,...,ₙ ∈ such that = ₁∘₂∘...∘ₙ; otherwise is irreducible in . 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.},
author = {Izak Broere, Samuel John Teboho Moagi, Peter Mihók, Roman Vasky},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {factorization; property of graphs; irreducible property; reducible property; lattice of properties of graphs; partition; irreducible properties},
language = {eng},
number = {2},
pages = {167-174},
title = {Factorizations of properties of graphs},
url = {http://eudml.org/doc/270424},
volume = {19},
year = {1999},
}

TY - JOUR
AU - Izak Broere
AU - Samuel John Teboho Moagi
AU - Peter Mihók
AU - Roman Vasky
TI - Factorizations of properties of graphs
JO - Discussiones Mathematicae Graph Theory
PY - 1999
VL - 19
IS - 2
SP - 167
EP - 174
AB - A property of graphs is any isomorphism closed class of simple graphs. For given properties of graphs ₁,₂,...,ₙ a vertex (₁, ₂, ...,ₙ)-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 $_i$. The class of all graphs having a vertex (₁, ₂, ...,ₙ)-partition is denoted by ₁∘₂∘...∘ₙ. A property is said to be reducible with respect to a lattice of properties of graphs if there are n ≥ 2 properties ₁,₂,...,ₙ ∈ such that = ₁∘₂∘...∘ₙ; otherwise is irreducible in . 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.
LA - eng
KW - factorization; property of graphs; irreducible property; reducible property; lattice of properties of graphs; partition; irreducible properties
UR - http://eudml.org/doc/270424
ER -