Enumeration and limit laws for series–parallel graphs

We show that the number gngn of labelled series–parallel graphs on nn vertices is asymptotically gn∼g⋅n−5/2γnn!gn∼g⋅n−5/2γnn!, where γγ and gg are explicit computable constants. We show that the number of edges in random series–parallel graphs is asymptotically normal with linear mean and variance, and that it is sharply concentrated around its expected value. Similar results are proved for labelled outerplanar graphs and for graphs not containing K2,3K2,3 as a minor.