Prime ideals in the lattice of additive induced-hereditary graph properties
Amelie J. Berger, Peter Mihók (2003)
Discussiones Mathematicae Graph Theory
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An additive induced-hereditary property of graphs is any class of finite simple graphs which is closed under isomorphisms, disjoint unions and induced subgraphs. The set of all additive induced-hereditary properties of graphs, partially ordered by set inclusion, forms a completely distributive lattice. We introduce the notion of the join-decomposability number of a property and then we prove that the prime ideals of the lattice of all additive induced-hereditary properties are divided...