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}
}
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. 
Highly Cited
This paper has 80 citations. REVIEW CITATIONS

Citations

Publications citing this paper.

80 Citations

051015'07'10'13'16'19
Citations per Year
Semantic Scholar estimates that this publication has 80 citations based on the available data.

See our FAQ for additional information.

References

Publications referenced by this paper.
Showing 1-8 of 8 references

On the Number of Edges in Random Planar Graphs

C. McDiarmid S. Gerke
Comb . Prob . and Computing • 2004

The number of 2 - connected labelled planar graphs

Z. Gao Bender, N. C. Wormald
Elec . J . Combinatorics Canonical Decomposition of Outerplanar Maps and Application to Enumeration , Coding and Generation , Springer Lecture Notes in Computer Science • 2003

Counting labelled trees, in: Canadian Mathematical Monographs

J. W. Moon
Canadian Mathematical Congress, Montreal, • 1970
View 1 Excerpt