Quasivarieties of graphs
type: Item
instance of: scholarly article
title: Quasivarieties of graphs
zbMATH Open document ID: 0849.08012
DOI: 10.1007/BF02106622
author: S. V. Sizyj
published in: Siberian Mathematical Journal
publication date: 1996-11-04T00:00:00Z
review text: By a graph we mean a model of a binary predicate \(\rho(x,y)\). Many well-known properties of binary relations, such as reflexivity, symmetry, antisymmetry, transitivity, etc., are written down by means of quasiidentities. Such important classes of graphs as the class of all partial orders, the class of models of an equivalence relation, the class of all trees, the class of all \(n\)-chromatic graphs, etc. are quasivarieties. Nevertheless, there are very few articles devoted to the study of graphs from the point of view of the theory of quasivarieties of algebraic systems. In the present article we continue the study, initiated by \textit{I. E. Benenson} [Izv. Vyssh. Uchebn. Zaved., Mat. 1979, No. 12(211), 14-20 (1979; Zbl 0432.08007)], of the lattices of quasivarieties and the bases of quasiidentities for some classes of graphs.
Mathematics Subject Classification ID: 08C15
Mathematics Subject Classification ID: 08B15
Mathematics Subject Classification ID: 05C99
Mathematics Subject Classification ID: 08C10
zbMATH DE Number: 917099
zbMATH Keywords: graph
zbMATH Keywords: model of a binary predicate
zbMATH Keywords: binary relations
zbMATH Keywords: partial orders
zbMATH Keywords: models of an equivalence relation
zbMATH Keywords: trees
zbMATH Keywords: \(n\)-chromatic graphs
zbMATH Keywords: lattices of quasivarieties
zbMATH Keywords: bases of quasiidentities
MaRDI profile type: Publication
cites work: Q3869409
cites work: The lattice of quasivarieties of semigroups
cites work: Covers in lattices of quasivarieties and independent axiomatizability
cites work: Quasivarieties of unars
cites work: Q3866167
description: scientific article; zbMATH DE number 917099