Asymptotic enumeration of labelled graphs by genus

作者：Bender Edward A^*; Gao Zhicheng

来源：Electronic Journal of Combinatorics, 2011, 18(1): P13.

We obtain asymptotic formulas for the number of rooted 2-connected and 3-connected surface maps on an orientable surface of genus g with respect to vertices and edges simultaneously. 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 k-connected graphs of orientable genus g for k <= 3.

• 出版日期2011-1-12