
 Embedding an outerplanar graph in a point set (Site not responding. Last check: ) 
  If the graph is disconnected, we can sort the point set by angle with some outside point (that is not in the point set), partition the point set appropriately, and embed the graph's connected components in the partitions of the point set. 
  If the graph is connected but has a cutvertex v, we can sort the point set by angle with some point p, partition the point set (excluding an extreme point p) appropriately, and embed the cut components of in the partitions, joining them at p. 
  In an outerplanar graph (remember, each bounded face is a triangle since we assume the graph is maximal), an (r,s)triangle is a face in the graph with at least one edge on the unbounded face such that deleting the vertices of the triangle cuts the graph into two outerplanar graphs of size r and s. 
 cgm.cs.mcgill.ca /~athens/cs507/Projects/2004/AndrewKing/507embedding.html (613 words) 
