Grobler, P. J. P.; Mynhardt, C. M. Upper domination parameters and edge-critical graphs. (English) Zbl 0959.05084 J. Comb. Math. Comb. Comput. 33, 239-251 (2000). Let \(\pi\) be one of the upper domination parameters \(\beta\), \(\Gamma\) or IR. The authors study graphs for which \(\pi\) decreases (\(\pi\)-edge-critical graphs) whenever an edge is added. They prove characterizations of \(\beta\)- and \(\Gamma\)-edge-critical graphs and show that a graph is IR-edge-critical if and only if it is \(\Gamma\)-edge-critical. Reviewer: Gregory Gutin (Egham) Cited in 3 Documents MSC: 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 05C75 Structural characterization of families of graphs Keywords:edge-critical graphs; domination; characterizations PDFBibTeX XMLCite \textit{P. J. P. Grobler} and \textit{C. M. Mynhardt}, J. Comb. Math. Comb. Comput. 33, 239--251 (2000; Zbl 0959.05084)