LIMIT POINTS FOR AVERAGE GENUS .2. 2-CONNECTED NONSIMPLICIAL GRAPHS

In part (I) of this paper, it was proved that there are no limit points for the set of values of average genus of 2-connected simplicial graphs and of 3-connected graphs. The need for such restrictions is now demonstrated by showing that infinitely many real numbers are limit points of values of average genus for 2-connected non-simplicial graphs. A systematic method for constructing such limit points is presented, and it is proved that this method is essentially the only way to construct limit points of values of average genus for "homeomorphically nested" 2-connected graphs. © 1992.