Geodesic
Minimal reducible bounds for hom-properties of graphs
Discussiones Mathematicae. Graph Theory, Tome 19 (1999) no. 2, pp. 143-158.

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Let H be a fixed finite graph and let → H be a hom-property, i.e. the set of all graphs admitting a homomorphism into H. We extend the definition of → H to include certain infinite graphs H and then describe the minimal reducible bounds for → H in the lattice of additive hereditary properties and in the lattice of hereditary properties.
Keywords: graph homomorphisms, minimal reducible bounds, additive hereditary graph property 
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Berger, Amelie; Broere, Izak. Minimal reducible bounds for hom-properties of graphs. Discussiones Mathematicae. Graph Theory, Tome 19 (1999) no. 2, pp. 143-158. http://geodesic.mathdoc.fr/item/DMGT_1999_19_2_a2/

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