Graphs admitting k-nu operations. part 2: The irreflexive case

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 H has finite duality if and only if H admits an NU polymorphism. This result allows the use of tree duals to generate the variety of digraphs admitting a k-NU polymorphism.