Abstract
For $n \geq 15$, we prove that the minimum number of triangles in an
$n$-vertex $K_4$-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, Erd\H{o}s, Holzman, and Krivelevich from 1996. Additionally, we show
that for any $s > r \geq 3$ and $t \geq 2 (s-2)+1$, there is a $K_s$-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 $K_r$. This shows that unlike the number of edges, the
number of $K_r$'s ($r >2$) in a $K_s$-saturated graph is not forced to grow
with the minimum degree, except for possibly in lower order terms.