Graphs Admitting $k$-NU Operations. Part 1: The Reflexive Case
Tomás Feder, Pavol Hell, Benoît Larose, Cynthia Loten, Mark Siggers, Claude Tardif · SIAM Journal on Discrete Mathematics · 2013
We describe a generating set for the variety of reflexive graphs that admit a compatible $k$-ary near-unanimity (NU) operation. We further delineate a very simple subset that generates the variety of $j$-absolute retracts; in particular we show that the class of reflexive graphs with a 4-NU operation coincides with the class of 3-absolute retracts. Our results generalize and encompass several results on NU-graphs and absolute retracts.