arXiv:0912.4670 Abstract | arXiv Analytics

arXiv:0912.4670 [math.CO]Abstract References Reviews Resources

Asymptotic enumeration of labelled graphs with a given genus

Published 2009-12-23, updated 2010-03-14Version 3

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.)

Comments: 28 pages; corrected, clarified & simplified presentation

Categories: math.CO

Subjects: 05C30

Keywords: labelled graphs, asymptotic enumeration, large face-width result, bivariate version, surface maps

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