Asymptotic enumeration of labelled graphs with a given genus
Combinatorics
2010-03-16 v3
Abstract
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.)
Keywords
Cite
@article{arxiv.0912.4670,
title = {Asymptotic enumeration of labelled graphs with a given genus},
author = {E. A. Bender and Z. Gao},
journal= {arXiv preprint arXiv:0912.4670},
year = {2010}
}
Comments
28 pages; corrected, clarified & simplified presentation