# Enumeration and limit laws for series-parallel graphs

@article{Bodirsky2007EnumerationAL, title={Enumeration and limit laws for series-parallel graphs}, author={Manuel Bodirsky and Omer Gim{\'e}nez and Mihyun Kang and Marc Noy}, journal={Eur. J. Comb.}, year={2007}, volume={28}, pages={2091-2105} }

- Published 2007 in Eur. J. Comb.
DOI:10.1016/j.ejc.2007.04.011

We show that the number gn of labelled series–parallel graphs on n vertices is asymptotically gn ∼ g · n−5/2γ nn!, where γ and g 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 K2,3 as a minor. c © 2007 Elsevier Ltd. All rights reserved.

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#### References

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Showing 1-8 of 8 references

## Counting labelled three-connected and homeomorphically irreducible two-connected graphs

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## Singularity Analysis of Generating Functions

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## Counting labelled trees, in: Canadian Mathematical Monographs

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