Unique factorization theorem and formal concept analysis

Authors:
Peter Mihók;Gabriel Semanišin
Affiliations:
Department of Applied Mathematics, Technical University Košice, Faculty of Economics, Košice, Slovak Republic and Mathematical Institute, Slovak Academy of Sciences, Košice, Slovak ...;Institute of Computer Science, P.J. Šafárik University, Faculty of Science, Košice, Slovak Republic
Venue:
CLA'06 Proceedings of the 4th international conference on Concept lattices and their applications
Year:
2006

Citing 6
Cited 0

Formal Concept Analysis: Mathematical Foundations

Formal Concept Analysis: Mathematical Foundations
Canonical Vertex Partitions

Combinatorics, Probability and Computing
Uniqueness and complexity in generalised colouring

Uniqueness and complexity in generalised colouring
Graph Theory With Applications

Graph Theory With Applications
Additive and hereditary properties of graphs are uniquely factorizable into irreducible factors

Journal of Graph Theory
Factorizations and characterizations of induced-hereditary and compositive properties

Journal of Graph Theory

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Abstract

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 a new, less complicated, proof of this theorem that is based on Formal Concept Analysis. The method of the proof can be successfully applied even for more general mathematical structures known as relational structures.