Discussiones Mathematicae Graph Theory 31(3) (2011) 559-575
doi: 10.7151/dmgt.1565

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UNIQUE FACTORIZATION THEOREM FOR OBJECT-SYSTEMS

Peter Mihók

Department of Applied Mathematics
Faculty of Economics, Technical University
B. Nemcovej, 040 01 Košice, Slovak Republic
and
Mathematical Institute, Slovak Academy of Science
Gresákova 6, 040 01 Košice, Slovak Republic
e-mail: peter.mihok@tuke.sk

Gabriel Semanišin

Institute of Computer Science
P.J. Safárik University, Faculty of Science
Jesenná 5, 041 54 Košice, Slovak Republic
e-mail: gabriel.semanisin@upjs.sk

Abstract

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.

2010 Mathematics Subject Classification: 05C15, 05C75.

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Received 7 April 2010
Revised 21 August 2010
Accepted 27 August 2010