Convex Geometries and The Copoint Graph

We introduce abstract convex geometries. Much as matroids can be thought of as "discrete vector spaces", convex geometries are "discrete convex hulls". There are specific convex sets of particular importance, called copoints. In 2006, Morris introduced a graph on the copoints where the cliques in this graph correspond to convexly independent sets in the convex geometry. We discuss results related to the chromatic number of this graph, both generally, and for planar point sets in general position.

Event Topic

Discrete Applied Math Seminar