Graphs Admitting $k$-NU Operations. Part 2: The Irreflexive Case
Abstract
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.
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© 2014, Society for Industrial and Applied Mathematics.
History
Submitted: 28 March 2013
Accepted: 31 January 2014
Published online: 3 June 2014
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Cited By
- Characterizing Bipartite Graphs Which Admit a k-NU Polymorphism via Absolute RetractsGraphs and Combinatorics, Vol. 37, No. 6 | 13 July 2021
- NU Polymorphisms on Reflexive DigraphsSIAM Journal on Discrete Mathematics, Vol. 32, No. 1 | 29 March 2018
- List-homomorphism problems on graphs and arc consistencyDiscrete Mathematics, Vol. 313, No. 22 | 1 Nov 2013
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