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Graph quasivarieties

Lehtonen, Erkko; Pöschel, Reinhard

Acta Sci. Math. (Szeged), 86 (2020), 31–50

Introduced by C. R. Shallon in 1979, graph algebras establish a useful connection between graph theory and universal algebra. This makes it possible to investigate graph varieties and graph quasivarieties, i.e., classes of graphs described by identities or quasi-identities. In this paper, graph quasivarieties are characterized as classes of graphs closed under directed unions of isomorphic copies of finite strong pointed subproducts.