On uniquely partitionable relational structures and object systems

• Volume: 26, Issue: 2, page 281-289
• ISSN: 2083-5892

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Abstract

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We introduce object systems as a common generalization of graphs, hypergraphs, digraphs and relational structures. Let C be a concrete category, a simple object system over C is an ordered pair S = (V,E), where E = A₁,A₂,...,Aₘ is a finite set of the objects of C, such that the ground-set $V\left({A}_{i}\right)$ of each object ${A}_{i}\in E$ is a finite set with at least two elements and $V\supseteq {\bigcup }_{i=1}^{m}V\left({A}_{i}\right)$. To generalize the results on graph colourings to simple object systems we define, analogously as for graphs, that an additive induced-hereditary property of simple object systems over a category C is any class of systems closed under isomorphism, induced-subsystems and disjoint union of systems, respectively. We present a survey of recent results and conditions for object systems to be uniquely partitionable into subsystems of given properties.

How to cite

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Jozef Bucko, and Peter Mihók. "On uniquely partitionable relational structures and object systems." Discussiones Mathematicae Graph Theory 26.2 (2006): 281-289. <http://eudml.org/doc/270588>.

@article{JozefBucko2006,
abstract = {We introduce object systems as a common generalization of graphs, hypergraphs, digraphs and relational structures. Let C be a concrete category, a simple object system over C is an ordered pair S = (V,E), where E = A₁,A₂,...,Aₘ is a finite set of the objects of C, such that the ground-set $V(A_i)$ of each object $A_i ∈ E$ is a finite set with at least two elements and $V ⊇ ⋃_\{i=1\}^m V(A_i)$. To generalize the results on graph colourings to simple object systems we define, analogously as for graphs, that an additive induced-hereditary property of simple object systems over a category C is any class of systems closed under isomorphism, induced-subsystems and disjoint union of systems, respectively. We present a survey of recent results and conditions for object systems to be uniquely partitionable into subsystems of given properties.},
author = {Jozef Bucko, Peter Mihók},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {graph; digraph; hypergraph; vertex colouring; uniquely partitionable system},
language = {eng},
number = {2},
pages = {281-289},
title = {On uniquely partitionable relational structures and object systems},
url = {http://eudml.org/doc/270588},
volume = {26},
year = {2006},
}

TY - JOUR
AU - Jozef Bucko
AU - Peter Mihók
TI - On uniquely partitionable relational structures and object systems
JO - Discussiones Mathematicae Graph Theory
PY - 2006
VL - 26
IS - 2
SP - 281
EP - 289
AB - We introduce object systems as a common generalization of graphs, hypergraphs, digraphs and relational structures. Let C be a concrete category, a simple object system over C is an ordered pair S = (V,E), where E = A₁,A₂,...,Aₘ is a finite set of the objects of C, such that the ground-set $V(A_i)$ of each object $A_i ∈ E$ is a finite set with at least two elements and $V ⊇ ⋃_{i=1}^m V(A_i)$. To generalize the results on graph colourings to simple object systems we define, analogously as for graphs, that an additive induced-hereditary property of simple object systems over a category C is any class of systems closed under isomorphism, induced-subsystems and disjoint union of systems, respectively. We present a survey of recent results and conditions for object systems to be uniquely partitionable into subsystems of given properties.
LA - eng
KW - graph; digraph; hypergraph; vertex colouring; uniquely partitionable system
UR - http://eudml.org/doc/270588
ER -

References

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