English

Characterizing Bipartite Graphs which Admit k-NU Polymorphisms via Absolute Retracts

Combinatorics 2016-09-06 v2

Abstract

We first introduce the class of bipartite absolute retracts with respect to tree obstructions with at most kk 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)(k+1)-ary near-unanimity (NU) polymorphism. This result mirrors the case for reflexive graphs and generalizes a known result for bipartite graphs admitting a 33-NU polymorphism.

Keywords

Cite

@article{arxiv.1608.06350,
  title  = {Characterizing Bipartite Graphs which Admit k-NU Polymorphisms via Absolute Retracts},
  author = {Adam Jaffe},
  journal= {arXiv preprint arXiv:1608.06350},
  year   = {2016}
}
R2 v1 2026-06-22T15:27:10.180Z