Random graphs on surfaces

10 years 6 months ago
Random graphs on surfaces
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.
Colin McDiarmid
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2008
Where JCT
Authors Colin McDiarmid
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