Berger, Amelie J.; Broere, Izak; Moagi, Samuel J. T.; Mihók, Peter Meet- and join-irreducibility of additive hereditary properties of graphs. (English) Zbl 1003.05101 Discrete Math. 251, No. 1-3, 11-18 (2002). Any class of simple graphs which is closed under subgraphs, isomorphisms, and unions is named an additive hereditary property of graphs. The set of all additive hereditary properties of graphs, partially ordered by set inclusion, is a lattice. The elements of this lattice which are meet-, join- and doubly-irreducible are studied. The authors discuss the significance of these elements for the lattice of ideals of this lattice. Reviewer: A.Rappoport (Landau) Cited in 3 Documents MSC: 05C99 Graph theory 06B10 Lattice ideals, congruence relations Keywords:property of graphs; irreducible property; reducible property; lattice of properties of graphs PDFBibTeX XMLCite \textit{A. J. Berger} et al., Discrete Math. 251, No. 1--3, 11--18 (2002; Zbl 1003.05101) Full Text: DOI