In a simple topological drawing of the complete graph $K_n$, vertices are mapped to points in the plane, edges are mapped to simple curves connecting the corresponding end points, and each pair of edges intersects at most once, either in a common vertex or in a proper crossing.
We discuss an axiomatization of simple drawings and for various sub-classes and present a SAT model. With the aid of modern SAT solvers, we investigate some famous and important classical theorems from Convex Geometry (such as Caratheodory’s, Helly's, Kirchberger's Theorem, and the Erdös-Szekeres Theorem) in the context of simple drawings.
This is joint work with Helena Bergold, Stefan Felsner, Felix Schröder, and Raphael Steiner.
Research is in progress.
Nov 25, 2019 | 04:00 PM s.t.
Freie Universität Berlin
Institut für Informatik
Room 005 (Ground Floor)