# On uniquely partitionable relational structures and object systems

Discussiones Mathematicae Graph Theory (2006)

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

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topJozef 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 -

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