Asymptotic enumeration and limit laws of planar graphs

@article{Gimnez2005AsymptoticEA,
  title={Asymptotic enumeration and limit laws of planar graphs},
  author={Omer Gim{\'e}nez and M. Noy},
  journal={Journal of the American Mathematical Society},
  year={2005},
  volume={22},
  pages={309-329}
}
A graph is planar if it can be embedded in the plane, or in the sphere, so that no two edges cross at an interior point. A planar graph together with a particular embedding is called a map. There is a rich theory of counting maps, started by Tutte in the 1960's. However, in this paper we are interested in counting graphs as combinatorial objects, regardless of how many nonequivalent topological embeddings they may have. As we are going to see, this makes the counting considerably more difficult… Expand
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