  We present upper and lower bounds for the number $i_n$ of interval graphs on
$n$ vertices. Answering a question posed by Hanlon, we show that the ordinary
generating function $I(x) = \sum_{n\ge 0} i_n\,x^n$ for the number $i_n$ of
$n$-vertex interval graphs has radius of convergence zero. We also show that
the exponential generating function $J(x) = \sum_{n\ge 0} i_n\,x^n/n!$ has
radius of convergence at least $1/2$.
