Enumeration and limit laws of series-parallel graphs
By Manuel Bodirsky, Omer Gimenez, Mihyun Kang, and Marc NoyEuropean Journal of Combinatorics, 28 (2007), 2091-2105
Abstract
We show that the number gn of labelled series-parallel graphs on n vertices is asymptotically gn ~ c n-5/2bn n!, where b and c 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 the number of edges is sharply concentrated around its expected value. Similar results are proved for labelled outerplanar graphs and for graphs not containing K2,3 as a minor.
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