Addisu Paulos: The Maximum Number of Paths of Length Three in a Planar Graph

Let f(n, H) denote the maximum number of copies of H possible in an
n-vertex planar graph. The function f(n, H) has been determined when
H is a cycle of length 3 or 4 by Hakimi and Schmeichel and when H is
a complete bipartite graph with smaller part of size 1 or 2 by Alon and
Caro. We determine f(n, H) exactly in the case when H is a path of
length 3.