Bounds on the maximum multiplicity of some common geometric graphs

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 general position (with no three points collinear): perfect matchings, spanning trees, spanning cycles (tours), and triangulations. (i) We present a new lower bound construction for the maximum number of triangulations a set of n points in general position can have. In particular, we show that a generalized double chain formed by two almost convex chains admits (8.65n ) different triangulations. This improves the bound (8.48n ) achieved by the previous best construction, the double zig-zag chain studied by Aichholzer et al.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Adrian Dumitrescu, André Schulz, Adam Sheffer, Csaba D. Tóth
• Keywords: Common Geometric Graphs, CORR 2010, Education, General Position, Lower Bound Construction