Bender, Edward A.; Gao, Zhicheng Asymptotic enumeration of labelled graphs by genus. (English) Zbl 1205.05013 Electron. J. Comb. 18, No. 1, Research Paper P13, 28 p. (2011). Summary: 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 facewidth 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 \(k \leq 3\). Cited in 6 Documents MSC: 05A16 Asymptotic enumeration 05C30 Enumeration in graph theory 05C78 Graph labelling (graceful graphs, bandwidth, etc.) 05C10 Planar graphs; geometric and topological aspects of graph theory Keywords:asymptotic formula; surface map; orientable surface; face width; labelled graphs; orientable genus PDFBibTeX XMLCite \textit{E. A. Bender} and \textit{Z. Gao}, Electron. J. Comb. 18, No. 1, Research Paper P13, 28 p. (2011; Zbl 1205.05013) Full Text: EuDML EMIS