  We consider three extremal problems about the number of copies of a fixed
graph in another larger graph. First, we correct an error in a result of Reiher
and Wagner and prove that the number of $k$-edge stars in a graph with density
$x \in [0, 1]$ is asymptotically maximized by a clique and isolated vertices or
its complement. Next, among ordered $n$-vertex graphs with $m$ edges, we
determine the maximum and minimum number of copies of a $k$-edge star whose
nonleaf vertex is minimum among all vertices of the star. Finally, for $s \ge
2$, we define a particular $3$-edge-colored complete graph $F$ on $2s$ vertices
with colors blue, green and red, and determine, for each $(x_b, x_g)$ with
$x_b+x_g\le 1$ and $x_b, x_g \ge 0$, the maximum density of $F$ in a large
graph whose blue, green and red edge sets have densities $x_b, x_g$ and
$1-x_b-x_g$, respectively. These are the first nontrivial examples of colored
graphs for which such complete results are proved.
