An additive hereditary graph property is any class of simple graphs, which is closed under isomorphisms unions and taking subgraphs. Let denote a class of all such properties. In the paper, we consider H-reducible over properties with H being a fixed graph. The finiteness of the sets of all minimal forbidden graphs is analyzed for such properties.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1446, author = {Ewa Drgas-Burchardt}, title = {Cardinality of a minimal forbidden graph family for reducible additive hereditary graph properties}, journal = {Discussiones Mathematicae Graph Theory}, volume = {29}, year = {2009}, pages = {263-274}, zbl = {1194.05132}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1446} }
Ewa Drgas-Burchardt. Cardinality of a minimal forbidden graph family for reducible additive hereditary graph properties. Discussiones Mathematicae Graph Theory, Tome 29 (2009) pp. 263-274. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1446/
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