On the maximum number of cycles in outerplanar and series-parallel graphs

Let c ( n ) be the maximum number of cycles in an outerplanar graph with n vertices. We show that lim c ( n ) 1 / n exists and equals β = 1.502837 … , where β is a constant related to the recurrence x n + 1 = 1 + x n 2 , x 0 = 1 . The same result holds for the larger class of series-parallel graphs.