Let denote a set of additive hereditary graph properties. It is a known fact that a partially ordered set is a complete distributive lattice. We present results when a join of two additive hereditary graph properties in has a finite or infinite family of minimal forbidden subgraphs.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1333, author = {Ewa Drgas-Burchardt}, title = {A note on joins of additive hereditary graph properties}, journal = {Discussiones Mathematicae Graph Theory}, volume = {26}, year = {2006}, pages = {413-418}, zbl = {1138.05060}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1333} }
Ewa Drgas-Burchardt. A note on joins of additive hereditary graph properties. Discussiones Mathematicae Graph Theory, Tome 26 (2006) pp. 413-418. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1333/
[000] [1] A.J. Berger, Minimal forbidden subgraphs of reducible graph properties, Discuss. Math. Graph Theory 21 (2001) 111-117, doi: 10.7151/dmgt.1136. | Zbl 0989.05060
[001] [2] A.J. Berger, I. Broere, S.J.T. Moagi and P. Mihók, Meet- and join-irreducibility of additive hereditary properties of graphs, Discrete Math. 251 (2002) 11-18, doi: 10.1016/S0012-365X(01)00323-5. | Zbl 1003.05101
[002] [3] M. Borowiecki and P. Mihók, Hereditary properties of graphs, in: V.R. Kulli, ed., Advances in Graph Theory (Vishawa International Publication, Gulbarga, 1991) 41-68.
[003] [4] I. Broere, M. Frick and G.Semanišin, Maximal graphs with respect to hereditary properties, Discuss. Math. Graph Theory 17 (1997) 51-66, doi: 10.7151/dmgt.1038. | Zbl 0902.05027
[004] [5] D.L. Greenwell, R.L. Hemminger and J. Klerlein, Forbidden subgraphs, Proceedings of the 4th S-E Conf. Combinatorics, Graph Theory and Computing (Utilitas Math., Winnipeg, Man., 1973) 389-394. | Zbl 0312.05128
[005] [6] J. Jakubik, On the Lattice of Additive Hereditary Properties of Finite Graphs, Discuss. Math. General Algebra and Applications 22 (2002) 73-86. | Zbl 1032.06003