Geodesic
On generating sets of induced-hereditary properties
Discussiones Mathematicae. Graph Theory, Tome 22 (2002) no. 1, pp. 183-192

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A natural generalization of the fundamental graph vertex-colouring problem leads to the class of problems known as generalized or improper colourings. These problems can be very well described in the language of reducible (induced) hereditary properties of graphs. It turned out that a very useful tool for the unique determination of these properties are generating sets. In this paper we focus on the structure of specific generating sets which provide the base for the proof of The Unique Factorization Theorem for induced-hereditary properties of graphs.
Keywords: induced-hereditary property of graphs, additivity, reducibility, generating sets, maximal graphs, unique factorization 
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Semanišin, Gabriel. On generating sets of induced-hereditary properties. Discussiones Mathematicae. Graph Theory, Tome 22 (2002) no. 1, pp. 183-192. http://geodesic.mathdoc.fr/item/DMGT_2002_22_1_a14/