Triangles in Ks-saturated graphs with minimum degree t

For n ≥ 15, we prove that the minimum number of triangles in an n-vertex K4-saturated graph with minimum degree 4 is exactly 2n-4, and that there is a unique extremal graph. This is a triangle version of a result of Alon, Erdos, Holzman, and Krivelevich from 1996. Additionally, we show that for any s \u3e r ≥ 3 and t ≥ 2 (s-2)+1, there is a Ks-saturated n-vertex graph with minimum degree t that has \binom{ s-2}{r-1}2^{r-1} n + c_{s,r,t} copies of Kr. This shows that unlike the number of edges, the number of Kr\u27s (r \u3e2) in a Ks-saturated graph is not forced to grow with the minimum degree, except for possibly in lower order terms