Geodesic
Cardinality of a minimal forbidden graph family for reducible additive hereditary graph properties
Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 2, pp. 263-274

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An additive hereditary graph property is any class of simple graphs, which is closed under isomorphisms unions and taking subgraphs. Let L^a denote a class of all such properties. In the paper, we consider H-reducible over L^a properties with H being a fixed graph. The finiteness of the sets of all minimal forbidden graphs is analyzed for such properties.
Keywords: hereditary graph property, lattice of additive hereditary graph properties, minimal forbidden graph family, join in the lattice, reducibility 
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     title = {Cardinality of a minimal forbidden graph family for reducible additive hereditary graph properties},
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Drgas-Burchardt, Ewa. Cardinality of a minimal forbidden graph family for reducible additive hereditary graph properties. Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 2, pp. 263-274. http://geodesic.mathdoc.fr/item/DMGT_2009_29_2_a4/