@article{, AUTHOR = {Drgas-Burchardt, Ewa}, TITLE = {Cardinality of a minimal forbidden graph family for reducible additive hereditary graph properties}, JOURNAL = {Discuss. Math. Graph Theory}, FJOURNAL = {Discussiones Mathematicae Graph Theory}, VOLUME = {29}, YEAR = {2009}, NUMBER = {2}, PAGES = {263-274}, ISSN = {1234-3099}, ABSTRACT = {An additive hereditary graph property is any class of simple graphs, which is closed under isomorphisms unions and taking subgraphs. Let ${\bf L}^{a}$ denote a class of all such properties. In the paper, we consider $H$-reducible over ${\bf L}^a$ properties with $H$ being a fixed graph. The finiteness of the sets of all minimal forbidden graphs is analyzed for such properties.},}