Which Venn diagrams can be drawn convexly?
by
Frank Ruskey
University of Victoria and University of Newcastle (visiting)
Coauthors: Bette Bultena (U. Victoria), Branko Grunbaum (U. Washington)

An n-Venn diagram is a collection of n simple curves in the plane with the property that they divide the plane into 2ⁿ connected regions, one region per possible intersection of the interiors of the curves. A Venn diagram is convex if there is a continuous tranformation of the plane that makes all n curves convex. We give a simple necessary and sufficient condition for a Venn diagram to be convex in terms of the directed dual graph of the diagram, namely that the dual must have a unique source and a unique sink.

Date received: November 8, 2000