Geodesic
Asymptotic enumeration of labelled graphs by genus
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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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 $k\le3$.
DOI : 10.37236/500
Classification : 05A16, 05C30, 05C78, 05C10
Mots-clés : asymptotic formula, surface map, orientable surface, face width, labelled graphs, orientable genus 
@article{10_37236_500,
     author = {Edward A. Bender and Zhicheng Gao},
     title = {Asymptotic enumeration of labelled graphs by genus},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/500},
     zbl = {1205.05013},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/500/}
}
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Edward A. Bender; Zhicheng Gao. Asymptotic enumeration of labelled graphs by genus. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/500

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