Geodesic
On uniquely partitionable relational structures and object systems
Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 2, pp. 281-289

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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.
Keywords: graph, digraph, hypergraph, vertex colouring, uniquely partitionable system 
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Bucko, Jozef; Mihók, Peter. On uniquely partitionable relational structures and object systems. Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 2, pp. 281-289. http://geodesic.mathdoc.fr/item/DMGT_2006_26_2_a9/