Topological Drawings meet SAT Solvers and Classical Theorems of Convex Geometry

Manfred Scheucher

TU Berlin

Abstract

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.