Unique Factorization Theorem and Formal Concept Analysis

摘要

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.