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On uniquely partitionable relational structures and object systems

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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 $V(A_i)$ 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.
Opis fizyczny
  • Department of Applied Mathematics, Faculty of Economics, Technical University, B. Nĕmcovej, 040 01 Košice, Slovak Republic
  • Department of Applied Mathematics, Faculty of Economics, Technical University, B. Nĕmcovej, 040 01 Košice, Slovak Republic
  • Mathematical Institute, Slovak Academy of Science, Gresákova 6, 040 01 Košice, Slovak Republic
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