On the factorization of reducible properties of graphs into irreducible factors

P. Mihók; R. Vasky

Discussiones Mathematicae Graph Theory (1995)

  • Volume: 15, Issue: 2, page 195-203
  • ISSN: 2083-5892

Abstract

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A hereditary property R of graphs is said to be reducible if there exist hereditary properties P₁,P₂ such that G ∈ R if and only if the set of vertices of G can be partitioned into V(G) = V₁∪V₂ so that ⟨V₁⟩ ∈ P₁ and ⟨V₂⟩ ∈ P₂. The problem of the factorization of reducible properties into irreducible factors is investigated.

How to cite

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P. Mihók, and R. Vasky. "On the factorization of reducible properties of graphs into irreducible factors." Discussiones Mathematicae Graph Theory 15.2 (1995): 195-203. <http://eudml.org/doc/270354>.

@article{P1995,
abstract = {A hereditary property R of graphs is said to be reducible if there exist hereditary properties P₁,P₂ such that G ∈ R if and only if the set of vertices of G can be partitioned into V(G) = V₁∪V₂ so that ⟨V₁⟩ ∈ P₁ and ⟨V₂⟩ ∈ P₂. The problem of the factorization of reducible properties into irreducible factors is investigated.},
author = {P. Mihók, R. Vasky},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {hereditary property of graphs; additivity; reducibility; vertex partition; hereditary property; factorization; reducible properties; factors},
language = {eng},
number = {2},
pages = {195-203},
title = {On the factorization of reducible properties of graphs into irreducible factors},
url = {http://eudml.org/doc/270354},
volume = {15},
year = {1995},
}

TY - JOUR
AU - P. Mihók
AU - R. Vasky
TI - On the factorization of reducible properties of graphs into irreducible factors
JO - Discussiones Mathematicae Graph Theory
PY - 1995
VL - 15
IS - 2
SP - 195
EP - 203
AB - A hereditary property R of graphs is said to be reducible if there exist hereditary properties P₁,P₂ such that G ∈ R if and only if the set of vertices of G can be partitioned into V(G) = V₁∪V₂ so that ⟨V₁⟩ ∈ P₁ and ⟨V₂⟩ ∈ P₂. The problem of the factorization of reducible properties into irreducible factors is investigated.
LA - eng
KW - hereditary property of graphs; additivity; reducibility; vertex partition; hereditary property; factorization; reducible properties; factors
UR - http://eudml.org/doc/270354
ER -

References

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  1. [1] M. Borowiecki, P. Mihók, Hereditary properties of graphs, in: V.R. Kulli, ed., Advances in Graph Theory (Vishwa International Publication, 1991) 42-69. 
  2. [2] T.R. Jensen and B. Toft, Graph Colouring Problems (Wiley-Interscience Publications, New York, 1995). Zbl0971.05046
  3. [3] P. Mihók, G. Semaniin, Reducible properties of graphs, Discussiones Math.- Graph Theory 15 (1995) 11-18, doi: 10.7151/dmgt.1002. 
  4. [4] P. Mihók, Additive hereditary properties and uniquely partitionable graphs, in: Graphs, Hypergraphs and Matroids (Zielona Góra, 1985) 49-58. Zbl0623.05043
  5. [5] P. Mihók, On the minimal reducible bound for outerplanar and planar graphs (to appear). Zbl0911.05043

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