For a simple graph H, →H denotes the class of all graphs that admit homomorphisms to H (such classes of graphs are called hom-properties). We investigate hom-properties from the point of view of the lattice of hereditary properties. In particular, we are interested in characterization of maximal graphs belonging to →H. We also provide a description of graphs maximal with respect to reducible hom-properties and determine the maximum number of edges of graphs belonging to →H.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1040, author = {Jan Kratochv\'\i l and Peter Mih\'ok and Gabriel Semani\v sin}, title = {Graphs maximal with respect to hom-properties}, journal = {Discussiones Mathematicae Graph Theory}, volume = {17}, year = {1997}, pages = {77-88}, zbl = {0905.05038}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1040} }
Jan Kratochvíl; Peter Mihók; Gabriel Semanišin. Graphs maximal with respect to hom-properties. Discussiones Mathematicae Graph Theory, Tome 17 (1997) pp. 77-88. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1040/
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