Meet- and join-irreducibility of additive hereditary properties of graphs Original Research Article

An additive hereditary property of graphs is any class of simple graphs which is closed under unions, subgraphs and isomorphisms. The set of all such properties is a lattice with set inclusion as the partial ordering. We study the elements of this lattice which are meet- join- and doubly-irreducible. The significance of these elements for the lattice of ideals of this lattice is discussed.