  We study multi-boundary correlators of Witten-Kontsevich topological gravity
in two dimensions. We present a method of computing an open string like
expansion, which we call the 't Hooft expansion, of the $n$-boundary correlator
for any $n$ up to any order by directly solving the KdV equation. We first
explain how to compute the 't Hooft expansion of the one-boundary correlator.
The algorithm is very similar to that for the genus expansion of the open free
energy. We next show that the 't Hooft expansion of correlators with more than
one boundaries can be computed algebraically from the correlators with a lower
number of boundaries. We explicitly compute the 't Hooft expansion of the
$n$-boundary correlators for $n=1,2,3$. Our results reproduce previously
obtained results for Jackiw-Teitelboim gravity and also the 't Hooft expansion
of the exact result of the three-boundary correlator which we calculate
independently in the Airy case.
