Eggleton, Roger B.; MacDougall, James A. Minimally triangle-saturated graphs: Adjoining a single vertex. (English) Zbl 0991.05058 Australas. J. Comb. 25, 263-278 (2002). A (finite, simple) graph is called triangle-saturated if adding any edge produces at least one new triangle (3-cycle). Using properties of dominating sets of vertices of a triangle-saturated graph \(G\), the authors investigate conditions under which a single vertex can be added to \(G\) so as to obtain a new triangle-saturated graph, and, in particular, conditions under which this extension is minimally saturated and primitive. The construction is applied to produce a family of primitive maximal triangle-free graphs, showing that the number of such graphs grows at least linearly with the number of vertices (while the growth rate is conjectured to be exponential). Reviewer: Herman J.Servatius (Worcester) Cited in 1 Document MSC: 05C35 Extremal problems in graph theory 05C38 Paths and cycles Keywords:triangle-saturated; triangle-free; dominating set PDFBibTeX XMLCite \textit{R. B. Eggleton} and \textit{J. A. MacDougall}, Australas. J. Comb. 25, 263--278 (2002; Zbl 0991.05058)