Random planar graphs


We study various properties of the random planar graph Rn, drawn uniformly at random from the classPn of all simple planar graphs on n labelled vertices. In particular, we show that the probability thatRn is connected is bounded away from 0 and from 1.We also show for example that each positive integer k, with high probability Rn has linearly many vertices of a given degree, in each embedding Rn has linearly many faces of a given size, and Rn has exponentially many automorphisms. © 2004 Elsevier Inc. All rights reserved.

DOI: 10.1016/j.jctb.2004.09.007

1 Figure or Table


Citations per Year

167 Citations

Semantic Scholar estimates that this publication has 167 citations based on the available data.

See our FAQ for additional information.

Cite this paper

@article{McDiarmid2005RandomPG, title={Random planar graphs}, author={Colin McDiarmid and Angelika Steger and Dominic J. A. Welsh}, journal={J. Comb. Theory, Ser. B}, year={2005}, volume={93}, pages={187-205} }