Author
McDiarmid, C
Journal title
Journal of Combinatorial Theory. Series B
DOI
10.1016/j.jctb.2007.11.006
Issue
4
Volume
98
Last updated
2022-03-07T10:55:10.877+00:00
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
Publication type
Journal Article
Publication date
1 July 2008
Please contact us with feedback and comments about this page. Created on 13 Oct 2016 - 17:14.