Feder, Tomás; Hell, Pavol; Larose, Benoît; Loten, Cynthia; Siggers, Mark; Tardif, Claude Graphs admitting \(k\)-NU operations. I: The reflexive case. (English) Zbl 1285.05152 SIAM J. Discrete Math. 27, No. 4, 1940-1963 (2013). Summary: 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. Cited in 1 ReviewCited in 5 Documents MSC: 05C75 Structural characterization of families of graphs 08B05 Equational logic, Mal’tsev conditions Keywords:near-unanimity operation; graphs PDFBibTeX XMLCite \textit{T. Feder} et al., SIAM J. Discrete Math. 27, No. 4, 1940--1963 (2013; Zbl 1285.05152) Full Text: DOI