# The order of uniquely partitionable graphs

Izak Broere; Marietjie Frick; Peter Mihók

Discussiones Mathematicae Graph Theory (1997)

- Volume: 17, Issue: 1, page 115-125
- ISSN: 2083-5892

## Access Full Article

top## Abstract

top## How to cite

topIzak Broere, Marietjie Frick, and Peter Mihók. "The order of uniquely partitionable graphs." Discussiones Mathematicae Graph Theory 17.1 (1997): 115-125. <http://eudml.org/doc/270714>.

@article{IzakBroere1997,

abstract = {Let ₁,...,ₙ be properties of graphs. A (₁,...,ₙ)-partition of a graph G is a partition V₁,...,Vₙ of V(G) such that, for each i = 1,...,n, the subgraph of G induced by $V_i$ has property $_i$. If a graph G has a unique (₁,...,ₙ)-partition we say it is uniquely (₁,...,ₙ)-partitionable. We establish best lower bounds for the order of uniquely (₁,...,ₙ)-partitionable graphs, for various choices of ₁,...,ₙ.},

author = {Izak Broere, Marietjie Frick, Peter Mihók},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {hereditary property of graphs; uniquely partitionable graphs; partition},

language = {eng},

number = {1},

pages = {115-125},

title = {The order of uniquely partitionable graphs},

url = {http://eudml.org/doc/270714},

volume = {17},

year = {1997},

}

TY - JOUR

AU - Izak Broere

AU - Marietjie Frick

AU - Peter Mihók

TI - The order of uniquely partitionable graphs

JO - Discussiones Mathematicae Graph Theory

PY - 1997

VL - 17

IS - 1

SP - 115

EP - 125

AB - Let ₁,...,ₙ be properties of graphs. A (₁,...,ₙ)-partition of a graph G is a partition V₁,...,Vₙ of V(G) such that, for each i = 1,...,n, the subgraph of G induced by $V_i$ has property $_i$. If a graph G has a unique (₁,...,ₙ)-partition we say it is uniquely (₁,...,ₙ)-partitionable. We establish best lower bounds for the order of uniquely (₁,...,ₙ)-partitionable graphs, for various choices of ₁,...,ₙ.

LA - eng

KW - hereditary property of graphs; uniquely partitionable graphs; partition

UR - http://eudml.org/doc/270714

ER -

## References

top- [1] G. Benadé, I. Broere, B. Jonck and M. Frick, Uniquely ${(m,k)}^{\tau}$-colourable graphs and k-τ-saturated graphs, Discrete Math. 162 (1996) 13-22, doi: 10.1016/0012-365X(95)00301-C. Zbl0870.05026
- [2] M. Borowiecki, P. Mihók, Hereditary properties of graphs, in: Advances in Graph Theory (Vishwa Internat. Publ., 1991) 41-68.
- [3] I. Broere and M. Frick, On the order of uniquely (k,m)-colourable graphs, Discrete Math. 82 (1990) 225-232, doi: 10.1016/0012-365X(90)90200-2. Zbl0712.05024
- [4] I. Broere, M. Frick and G. Semanišin, Maximal graphs with respect to hereditary properties, Discussiones Mathematicae Graph Theory 17 (1997) 51-66, doi: 10.7151/dmgt.1038. Zbl0902.05027
- [5] G. Chartrand and L. Lesniak, Graphs and Digraphs (Second Edition, Wadsworth & Brooks/Cole, Monterey, 1986). Zbl0666.05001
- [6] M. Frick, On replete graphs, J. Graph Theory 16 (1992) 165-175, doi: 10.1002/jgt.3190160208. Zbl0763.05044
- [7] M. Frick and M.A. Henning, Extremal results on defective colourings of graphs, Discrete Math. 126 (1994) 151-158, doi: 10.1016/0012-365X(94)90260-7. Zbl0794.05029
- [8] P. Mihók, Additive hereditary properties and uniquely partitionable graphs, in: Graphs, Hypergraphs and Matroids (Zielona Góra, 1985) 49-58. Zbl0623.05043
- [9] P. Mihók and G. Semanišin, Reducible properties of graphs, Discussiones Math. Graph Theory 15 (1995) 11-18, doi: 10.7151/dmgt.1002. Zbl0829.05057

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.