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.
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