Counting Triangulations of Planar Point Sets

@article{Sharir2011CountingTO,
  title={Counting Triangulations of Planar Point Sets},
  author={Micha Sharir and Adam Sheffer and Emo Welzl},
  journal={Electr. J. Comb.},
  year={2011},
  volume={18}
}
We study the maximal number of triangulations that a planar set of n points can have, and show that it is at most 30n. This new bound is achieved by a careful optimization of the charging scheme of Sharir and Welzl (2006), which has led to the previous best upper bound of 43n for the problem. Moreover, this new bound is useful for bounding the number of other types of planar (i.e., crossing-free) straight-line graphs on a given point set. Specifically, we derive new upper bounds for the number… CONTINUE READING