Geodesic
Graphs maximal with respect to hom-properties
Discussiones Mathematicae. Graph Theory, Tome 17 (1997) no. 1, pp. 77-88

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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.
Keywords: hom-property of graphs, hereditary property of graphs, maximal graphs 
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     title = {Graphs maximal with respect to hom-properties},
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Kratochvíl, Jan; Mihók, Peter; Semanišin, Gabriel. Graphs maximal with respect to hom-properties. Discussiones Mathematicae. Graph Theory, Tome 17 (1997) no. 1, pp. 77-88. http://geodesic.mathdoc.fr/item/DMGT_1997_17_1_a3/