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{\bf Edward A. Bender and Zhicheng Gao}
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{\bf Asymptotic Enumeration of Labelled Graphs by Genus}
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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 $k\le3$.
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