Name
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. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1016/j.jctb.2007.11.006 | J. Comb. Theory, Ser. B |
Keywords | Field | DocType |
graphs embeddable,random graph,planar,labelled planar graph,random labelled planar graph,embeddable,small planar component,enumeration,labelled,labelled graphs embeddable,planar graph,giant component,surface,unlabelled graph,fixed surface | Discrete mathematics,Random regular graph,Indifference graph,Combinatorics,Random graph,Chordal graph,Clique-sum,Pathwidth,1-planar graph,Mathematics,Maximal independent set | Journal |
Volume | Issue | ISSN |
98 | 4 | Journal of Combinatorial Theory, Series B |
Citations | PageRank | References |
15 | 1.10 | 20 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Colin McDiarmid | 1 | 1071 | 167.05 |