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 $kle3$.
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机译：我们获得了$ g $属可定向曲面上同时针对顶点和边的生根2连通和3连通曲面图的渐近公式。我们还为随机3连通图得出了较大脸部宽度结果的双变量版本。然后，将这些结果用于为$ k le3 $的可定向属$ g $标记的$ k $连接图的数量导出渐近公式。
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