Geodesic
Unique factorization theorem for object-systems
Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 3, pp. 559-575

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The concept of an object-system is a common generalization of simple graph, digraph and hypergraph. In the theory of generalised colourings of graphs, the Unique Factorization Theorem (UFT) for additive induced-hereditary properties of graphs provides an analogy of the well-known Fundamental Theorem of Arithmetics. The purpose of this paper is to present UFT for object-systems. This result generalises known UFT for additive induced-hereditary and hereditary properties of graphs and digraphs. Formal Concept Analysis is applied in the proof.
Keywords: object-system, unique factorization, graph, hypergraph, formal concept analysis 
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Mihók, Peter; Semanišin, Gabriel. Unique factorization theorem for object-systems. Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 3, pp. 559-575. http://geodesic.mathdoc.fr/item/DMGT_2011_31_3_a10/