We study digraphs preserved by a Maltsev operation: Maltsev digraphs. We show that these digraphs retract either onto a directed path or to the disjoint union of directed cycles, showing in this way that the constraint satisfaction problem for Maltsev digraphs is in logspace, L. We then generalize results from Kazda (2011) to show that a Maltsev digraph is preserved not only by a majority opera...

Maltsev families of varieties which are closed under join or Maltsev product are investigated. New Maltsev conditions for congruence semi-distributivity are given.

Tame congruence theory identifies six Maltsev conditions associated with locally finite varieties omitting certain types of local behaviour. Extending a result of Siggers, we show that of these six Maltsev conditions only two of them are equivalent to strong Maltsev conditions for locally finite varieties. Besides omitting the unary type [24], the only other of these conditions that is strong i...

In this paper we investigate the computational complexity of deciding if a given finite algebraic structure satisfies a certain type of existential condition on its set of term operations. These conditions, known as Maltsev conditions, have played a central role in the classification, study, and applications of general algebraic structures. Several well studied properties of equationally define...

In this article, we provide a new algorithm for solving constraint satisfaction problems with Maltsev constraints, based on the new notion of Maltsev consistency.

We give an abstract characterization of categories which are localizations of Maltsev varieties. These results can be applied to characterize localizations of naturally Maltsev varieties.

We give an abstract characterization of categories which are localiza-tions of Maltsev varieties. These results can be applied to characterize localizations of naturally Maltsev varieties.

Second order conservative languages with a Maltsev polymorphism also have a majority polymorphism. Abstract The paper proves that for any second order conservative constraint language with a Maltsev polymorphism there is a majority polymor-phism. Moreover, the majority polymorphism can be defined by the Maltsev polymorphism.

Tame congruence theory identifies six Maltsev conditions associated with locally finite varieties omitting certain subsets of types of local behaviour. Extending a result of Siggers, we show that of these six Maltsev conditions only two of them are equivalent to strong Maltsev conditions for locally finite varieties. Besides omitting the unary type [18], the only other of these conditions that ...