Asymptotic enumerations for rooted planar maps and rooted outerplanar maps (Q1177278)

Map refers to rooted planar map. It is proved that almost all maps are not outerplanar, and the same is proved for some restricted maps, like loopless maps, simple maps, and non-separable maps. Almost all outerplanar maps are not trees, and the same holds for some restricted outerplanar maps, like loopless and simple maps. The method of proof is the asymptotic evaluation of exact enumeration results from \textit{E. A. Bender} and \textit{L. B. Richmond} [J. Comb. Theory, Ser. B 40, 297-329 (1986; Zbl 0563.05033)]. The author claims the same results for unrooted maps.