This article is cited in 6 papers

Quasivarieties of graphs and independent axiomatizability

A. V. Kravchenko^abc, A. V. Yakovlev<sup>b

a</sup> Sobolev Institute of Mathematics, Novosibirsk, Russia
^b Novosibirsk State University, Novosibirsk, Russia
^c Siberian Institute of Management (Department of RANEPA), Novosibirsk, Russia

Abstract: In the present article, we continue to study the complexity of the lattice of quasivarieties of graphs. For every quasivariety $\mathbf{K}$ of graphs that contains a non-bipartite graph, we find a subquasivariety $\mathbf{K}^\prime\subseteq\mathbf{K}$ such that there exist $2^\omega$ subquasivarieties $\mathbf{K}^{\prime\prime}\in\mathrm{L_q}(\mathbf{K}^\prime)$ without covers (hence, without independent bases for their quasi-identities in $\mathbf{K}^\prime$).

Key words: quasivariety, graph, basis for quasi-identities.

UDC: 512.57

Received: 13.02.2017

DOI: 10.17377/mattrudy.2017.20.204

 English version: Siberian Advances in Mathematics, 2018, 28:1, 53–59

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