Displaying similar documents to “Prime ideals in the lattice of additive induced-hereditary graph properties”

On the lattice of additive hereditary properties of finite graphs

Ján Jakubík (2002)

Discussiones Mathematicae - General Algebra and Applications

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In this paper it is proved that the lattice of additive hereditary properties of finite graphs is completely distributive and that it does not satisfy the Jordan-Dedekind condition for infinite chains.

Minimal reducible bounds for hom-properties of graphs

Amelie Berger, Izak Broere (1999)

Discussiones Mathematicae Graph Theory

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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.

A survey of hereditary properties of graphs

Mieczysław Borowiecki, Izak Broere, Marietjie Frick, Peter Mihók, Gabriel Semanišin (1997)

Discussiones Mathematicae Graph Theory

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In this paper we survey results and open problems on the structure of additive and hereditary properties of graphs. The important role of vertex partition problems, in particular the existence of uniquely partitionable graphs and reducible properties of graphs in this structure is emphasized. Many related topics, including questions on the complexity of related problems, are investigated.