# Uniquely partitionable planar graphs with respect to properties having a forbidden tree

Discussiones Mathematicae Graph Theory (1999)

- Volume: 19, Issue: 1, page 71-78
- ISSN: 2083-5892

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topJozef Bucko, and Jaroslav Ivančo. "Uniquely partitionable planar graphs with respect to properties having a forbidden tree." Discussiones Mathematicae Graph Theory 19.1 (1999): 71-78. <http://eudml.org/doc/270406>.

@article{JozefBucko1999,

abstract = {Let ₁, ₂ be graph properties. A vertex (₁,₂)-partition of a graph G is a partition V₁,V₂ of V(G) such that for i = 1,2 the induced subgraph $G[V_i]$ has the property $_i$. A property ℜ = ₁∘₂ is defined to be the set of all graphs having a vertex (₁,₂)-partition. A graph G ∈ ₁∘₂ is said to be uniquely (₁,₂)-partitionable if G has exactly one vertex (₁,₂)-partition. In this note, we show the existence of uniquely partitionable planar graphs with respect to hereditary additive properties having a forbidden tree.},

author = {Jozef Bucko, Jaroslav Ivančo},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {uniquely partitionable planar graphs; forbidden graphs; partition; planar graphs; hereditary additive properties; forbidden tree},

language = {eng},

number = {1},

pages = {71-78},

title = {Uniquely partitionable planar graphs with respect to properties having a forbidden tree},

url = {http://eudml.org/doc/270406},

volume = {19},

year = {1999},

}

TY - JOUR

AU - Jozef Bucko

AU - Jaroslav Ivančo

TI - Uniquely partitionable planar graphs with respect to properties having a forbidden tree

JO - Discussiones Mathematicae Graph Theory

PY - 1999

VL - 19

IS - 1

SP - 71

EP - 78

AB - Let ₁, ₂ be graph properties. A vertex (₁,₂)-partition of a graph G is a partition V₁,V₂ of V(G) such that for i = 1,2 the induced subgraph $G[V_i]$ has the property $_i$. A property ℜ = ₁∘₂ is defined to be the set of all graphs having a vertex (₁,₂)-partition. A graph G ∈ ₁∘₂ is said to be uniquely (₁,₂)-partitionable if G has exactly one vertex (₁,₂)-partition. In this note, we show the existence of uniquely partitionable planar graphs with respect to hereditary additive properties having a forbidden tree.

LA - eng

KW - uniquely partitionable planar graphs; forbidden graphs; partition; planar graphs; hereditary additive properties; forbidden tree

UR - http://eudml.org/doc/270406

ER -

## References

top- [1] J. Bucko, M. Frick, P. Mihók and R. Vasky, Uniquely partitionable graphs, Discuss. Math. Graph Theory 17 (1997) 103-114, doi: 10.7151/dmgt.1043. Zbl0906.05057
- [2] J. Bucko, P. Mihók and M. Voigt, Uniquely partitionable planar graphs, Discrete Math. 191 (1998) 149-158, doi: 10.1016/S0012-365X(98)00102-2. Zbl0957.05029
- [3] M. Borowiecki, J. Bucko, P. Mihók, Z. Tuza and M. Voigt, Remarks on the existence of uniquely partitionable planar graphs, 13. Workshop on Discrete Optimization, Burg, abstract, 1998.
- [4] P. Mihók, Additive hereditary properties and uniquely partitionable graphs, in: M. Borowiecki and Z. Skupień, eds., Graphs, hypergraphs and matroids (Zielona Góra, 1985) 49-58. Zbl0623.05043

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