Asymptotic enumeration of labelled graphs with a given genus

Details Asymptotic enumeration of labelled graphs with a given genus Asymptotic enumeration of labelled graphs with a given genus

2009-12-23

arxiv.org/abs/0912.4670v3

Mathematics

Combinatorics

28 pages; corrected, clarified & simplified presentation

Scientific paper

We enumerate rooted 2-connected and 3-connected surface maps with respect to
vertices and edges. We also derive the bivariate version of the large
face-width result for random 3-connected maps. These results are then used to
derive asymptotic formulas for the number of labelled graphs of genus g
(1-connected, 2-connected, and 3-connected graphs.)

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