Submaps of maps. III. k-Connected nonplanar maps

Edward A Bender, L.Bruce Richmond
1992 Journal of combinatorial theory. Series B (Print)  
We study 3-connected maps, 3-connected triangulations. and simple triangulations on arbitrary surfaces. It is shown that the radii of convergence do not depend on the surface and that the number of maps grows in a smooth manner. This is used to show that any possible planar submap occurs many times as a submap of almost all maps of any of the three types mentioned. By studying 3-connected maps in more detail, we show that nonplanar submaps of them are rare.
doi:10.1016/0095-8956(92)90036-w fatcat:lxawkh3agfhtnl3cv5hcnybg64