# DIMACS Discrete Math/Theory of Computing Seminar

## Title:

Planar Graph Models, Hamiltonian Cycles and Jordan Curves

## Speaker:

- Peter Hamburger
- Indiana-Purdue University

## Place:

- Seminar Room 431, CoRE Building,
- Rutgers University

## Time:

- 4:30 PM
- Tuesday, October 22, 1996

Abstract:
Using topological graph theory, planar and spherical graph models, and
Hamiltonian cycles we developed methods to investigate special families
of simple closed Jordan curves on the plane as well as on the sphere.
Utilizing these procedures we answered several problems and conjectures
of Grunbaum on Venn diagrams and independent families of sets. One of
our results corrects some erroneous statements that started with John
Venn more than a century ago in 1880 and have been repeated frequently
by others since then. An other one answers Grunbaum's conjecture: Every
Venn diagram of n curves can be extended to a Venn diagram of n+1 curves
by the addition of a suitable simple closed Jordan curve. This problem
also goes back to Venn itself. We also will discuse one of Peter
Winkler's related conjectures. Convex and strongly convex Venn diagrams
will be studied as well. Some of the results are joint results with K.
B. Chilakamarri and/or R. E. Pippert, Indiana-Purdue University Fort
Wayne.

Document last modified on October 14, 1996