# Reducible properties of graphs

• Volume: 15, Issue: 1, page 11-18
• ISSN: 2083-5892

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## Abstract

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Let L be the set of all hereditary and additive properties of graphs. For P₁, P₂ ∈ L, the reducible property R = P₁∘P₂ is defined as follows: G ∈ R if and only if there is a partition V(G) = V₁∪ V₂ of the vertex set of G such that $⟨V₁{⟩}_{G}\in P₁$ and $⟨V₂{⟩}_{G}\in P₂$. The aim of this paper is to investigate the structure of the reducible properties of graphs with emphasis on the uniqueness of the decomposition of a reducible property into irreducible ones.

## How to cite

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P. Mihók, and G. Semanišin. "Reducible properties of graphs." Discussiones Mathematicae Graph Theory 15.1 (1995): 11-18. <http://eudml.org/doc/270454>.

@article{P1995,
abstract = {Let L be the set of all hereditary and additive properties of graphs. For P₁, P₂ ∈ L, the reducible property R = P₁∘P₂ is defined as follows: G ∈ R if and only if there is a partition V(G) = V₁∪ V₂ of the vertex set of G such that $⟨V₁⟩_G ∈ P₁$ and $⟨V₂⟩_G ∈ P₂$. The aim of this paper is to investigate the structure of the reducible properties of graphs with emphasis on the uniqueness of the decomposition of a reducible property into irreducible ones.},
author = {P. Mihók, G. Semanišin},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {hereditary property of graphs; additivity; reducibility; additive properties of graphs; reducible property; hereditary property; cancellation problem},
language = {eng},
number = {1},
pages = {11-18},
title = {Reducible properties of graphs},
url = {http://eudml.org/doc/270454},
volume = {15},
year = {1995},
}

TY - JOUR
AU - P. Mihók
AU - G. Semanišin
TI - Reducible properties of graphs
JO - Discussiones Mathematicae Graph Theory
PY - 1995
VL - 15
IS - 1
SP - 11
EP - 18
AB - Let L be the set of all hereditary and additive properties of graphs. For P₁, P₂ ∈ L, the reducible property R = P₁∘P₂ is defined as follows: G ∈ R if and only if there is a partition V(G) = V₁∪ V₂ of the vertex set of G such that $⟨V₁⟩_G ∈ P₁$ and $⟨V₂⟩_G ∈ P₂$. The aim of this paper is to investigate the structure of the reducible properties of graphs with emphasis on the uniqueness of the decomposition of a reducible property into irreducible ones.
LA - eng
KW - hereditary property of graphs; additivity; reducibility; additive properties of graphs; reducible property; hereditary property; cancellation problem
UR - http://eudml.org/doc/270454
ER -

## References

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1. [1] V. E. Alekseev, Range of values of entropy of hereditary classes of graphs, Diskretnaja matematika 4 (1992) 148-157 (Russian). Zbl0766.05088
2. [2] M. Borowiecki, P. Mihók, Hereditary properties of graphs in: Advances in Graph Theory, Vishwa International Publication, India, (1991) 42-69.
3. [3] G. Chartrand, L. Lesniak, Graphs and Digraphs (Wadsworth & Brooks/Cole, Monterey California 1986). Zbl0666.05001
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5. [5] P. Mihók, An extension of Brook's theorem, Annals of Discrete Math. 51 (1992) 235-236. Zbl0766.05028
6. [6] P. Mihók, On the minimal reducible bound for outerplanar and planar graphs, (to appear). Zbl0911.05043
7. [7] M. Simonovits, Extremal graph theory, in: L. W. Beineke and R. J. Wilson eds. Selected Topics in Graph Theory 2 (Academic Press, London, 1983) 161-200.
8. [8] E. R. Scheinerman, On the structure of hereditary classes of graphs, Journal of Graph Theory 10 (1986) 545-551, doi: 10.1002/jgt.3190100414. Zbl0609.05057
9. [9] E. R. Scheinerman, J. Zito, On the size of hereditary classes of graphs, J. Combin. Theory (B) 61 (1994) 16-39, doi: 10.1006/jctb.1994.1027. Zbl0811.05048

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