On the enumeration of interval graphs
Joyce C. Yang, Nicholas J. Pippenger · Proceedings of the American Mathematical Society Series B · 2017
We present upper and lower bounds for the number i n i_n of interval graphs on n n vertices. Answering a question posed by Hanlon, we show that the ordinary generating function I ( x ) = ∑ n ≥ 0 i n x n I(x) = \sum _{n\ge 0} i_n\,x^n for the number i n i_n of n n -vertex interval graphs has radius of convergence zero. We also show that the exponential generating function J ( x ) = ∑ n ≥ 0 i n x n / n ! J(x) = \sum _{n\ge 0} i_n\,x^n/n! has radius of convergence at least 1 / 2 1/2 .