On the Number of Pseudo-Triangulations of Certain Point Sets

Oswin Aichholzer, David Orden, Francisco Santos, Bettina Speckmann

Published 2006-01-31, updated 2007-06-14Version 2

We pose a monotonicity conjecture on the number of pseudo-triangulations of any planar point set, and check it on two prominent families of point sets, namely the so-called double circle and double chain. The latter has asymptotically $12^n n^{\Theta(1)}$ pointed pseudo-triangulations, which lies significantly above the maximum number of triangulations in a planar point set known so far.