Random graphs on surfaces

Author: 

McDiarmid, C

Publication Date: 

1 July 2008

Journal: 

Journal of Combinatorial Theory. Series B

Last Updated: 

2019-04-26T05:26:54.863+01:00

Issue: 

4

Volume: 

98

DOI: 

10.1016/j.jctb.2007.11.006

page: 

778-797

abstract: 

Counting labelled planar graphs, and typical properties of random labelled planar graphs, have received much attention recently. We start the process here of extending these investigations to graphs embeddable on any fixed surface S. In particular we show that the labelled graphs embeddable on S have the same growth constant as for planar graphs, and the same holds for unlabelled graphs. Also, if we pick a graph uniformly at random from the graphs embeddable on S which have vertex set {1, ..., n}, then with probability tending to 1 as n → ∞, this random graph either is connected or consists of one giant component together with a few nodes in small planar components. © 2007 Elsevier Inc. All rights reserved.

Symplectic id: 

102286

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article