×

Graphs admitting \(k\)-NU operations. I: The reflexive case. (English) Zbl 1285.05152

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.

MSC:

05C75 Structural characterization of families of graphs
08B05 Equational logic, Mal’tsev conditions
PDFBibTeX XMLCite
Full Text: DOI