Gorbunov, Viktor; Kravchenko, Alexandr Antivarieties and colour-families of graphs. (English) Zbl 1058.08009 Algebra Univers. 46, No. 1-2, 43-67 (2001). The authors suggest an algebraic approach to the study of colour-families of graphs. This approach is based on the notion of a congruence of an arbitrary structure. They prove that every colour-family of graphs is a finitely generated universal Horn class and show that for every colour-family the universal theory is dedicable. They study the structure of the lattice of colour-families of graphs and the lattice of antivarieties of graphs. They also consider bases of quasi-identities and bases of anti-identities for colour-families and find certain relations between the existence of bases of a special form and problems in graph theory. Reviewer: Ivan Chajda (Olomouc) Cited in 1 ReviewCited in 7 Documents MSC: 08C15 Quasivarieties 03B25 Decidability of theories and sets of sentences 05C15 Coloring of graphs and hypergraphs 05C75 Structural characterization of families of graphs 03C05 Equational classes, universal algebra in model theory Keywords:universal Horn class; quasivariety; colour-family; graph; relational structure PDFBibTeX XMLCite \textit{V. Gorbunov} and \textit{A. Kravchenko}, Algebra Univers. 46, No. 1--2, 43--67 (2001; Zbl 1058.08009)