Counting Carambolas
  We give upper and lower bounds on the maximum and minimum number of geometric configurations of various kinds present (as subgraphs) in a triangulation of $n$ points in the plane. Configurations of interest include \emph{convex polygons}, \emph{star-shaped polygons} and \emph{monotone paths}. We also consider related problems for \emph{directed} planar straight-line graphs. 
Adrian Dumitrescu, Maarten L\"offler, Andr\'e Schulz, and Csaba D.   T\'oth
math.CO cs.DM