English

The evolution of uniform random planar graphs

Combinatorics 2011-01-27 v1

Abstract

Let P_{n,m} denote the graph taken uniformly at random from the set of all planar graphs on {1,2,..., n} with exactly m(n) edges. We use counting arguments to investigate the probability that P_{n,m} will contain given components and subgraphs, finding that there is different asymptotic behaviour depending on the ratio m/n.

Keywords

Cite

@article{arxiv.1101.5110,
  title  = {The evolution of uniform random planar graphs},
  author = {Chris Dowden},
  journal= {arXiv preprint arXiv:1101.5110},
  year   = {2011}
}

Comments

20 pages, 11 figures

R2 v1 2026-06-21T17:17:27.194Z