Feder, Tomás; Hell, Pavol; Larose, Benoît; Siggers, Mark; Tardif, Claude Graphs admitting \(k\)-NU operations. II: The irreflexive case. (English) Zbl 1298.05272 SIAM J. Discrete Math. 28, No. 2, 817-834 (2014). Summary: We describe a generating set for the variety of simple graphs that admit a \(k\)-ary near-unanimity (NU) polymorphism. The result follows from an analysis of NU polymorphisms of strongly bipartite digraphs, i.e., whose vertices are either a source or a sink. We show that the retraction problem for a strongly bipartite digraph \({\mathbb H}\) has finite duality if and only if \({\mathbb H}\) admits an NU polymorphism. This result allows the use of tree duals to generate the variety of digraphs admitting a \(k\)-NU polymorphism.For Part I see [Zbl 1285.05152]. Cited in 5 Documents MSC: 05C75 Structural characterization of families of graphs 08B05 Equational logic, Mal’tsev conditions Keywords:near-unanimity polymorphism; graphs; strongly bipartite digraphs; finite duality Citations:Zbl 1285.05152 PDFBibTeX XMLCite \textit{T. Feder} et al., SIAM J. Discrete Math. 28, No. 2, 817--834 (2014; Zbl 1298.05272) Full Text: DOI