Random planar graphs

Abstract

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

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@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} }