Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Thursday, April 28, 2016, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Manuel Wettstein

Crossing-free Geometric Graphs on Wheel Sets

A _wheel set_ is a set of n+1 points in the Euclidean plane, n points in convex position and one extra point which can be placed arbitrarily in the interior. We consider the problem of counting the number of crossing-free geometric graphs on such point sets.

In previous work by Ruiz-Vargas and Welzl, a simple formula was proved for the special case of perfect matchings. We generalize this result to arbitrary families of graphs (triangulations, spanning trees, and more). We further note that the formula only depends on what we call the _frequency vector_ of P and not the whole order type information. While the number of distinct order types for wheel sets is roughly 2^n, the number of frequency vectors is much smaller, namely 2^{n/2}.

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