Characterizing Bipartite Graphs Which Admit a k-NU Polymorphism via Absolute Retracts.

We first introduce the class of bipartite absolute retracts with respect to tree obstructions with at most k leaves. Then, using the theory of homomorphism duality, we show that this class of absolute retracts coincides exactly with the bipartite graphs which admit a (k + 1) -ary near-unanimity polymorphism. This result mirrors the case for reflexive graphs and generalizes a known result for bipartite graphs which admit a 3-ary near-unanimity polymorphism. [ABSTRACT FROM AUTHOR]