Geodesic
Quasivarieties of graphs and independent axiomatizability
Matematičeskie trudy, Tome 20 (2017) no. 2, pp. 80-89.

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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 $\mathbf{K}^\prime$). 
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A. V. Kravchenko; A. V. Yakovlev. Quasivarieties of graphs and independent axiomatizability. Matematičeskie trudy, Tome 20 (2017) no. 2, pp. 80-89. http://geodesic.mathdoc.fr/item/MT_2017_20_2_a3/

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