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...
Oswin Aichholzer, David Orden, Francisco Santos, B...
We give a brief account of results concerning the number of triangulations on finite point sets in the plane, both for arbitrary sets and for specific sets such as the n
Abstract. We show that there is a matching between the edges of any two triangulations of a planar point set such that an edge of one triangulation is matched either to the identic...
Oswin Aichholzer, Franz Aurenhammer, Michael Tasch...
We introduce the concept of a constrained pointed pseudo-triangulation TG of a point set S with respect to a pointed planar straight line graph G = (S, E). For the case that G for...
Oswin Aichholzer, Michael Hoffmann, Bettina Speckm...
We obtain new lower and upper bounds for the maximum multiplicity of some weighted and, respectively, non-weighted common geometric graphs drawn on n points in the plane in genera...