A classical and well-studied problem from graph theory is to find a longest circle in planar graphs. An obvious way to find such a circle is to start with a small circle and extend it step by step. Until now, no method was known that implements this in this generality, but it was recently shown in this result  about the dynamics of circles in polyhedral graphs (joint-work with Jan Kessler).
In this Master’s thesis, this result will be strengthened in different directions. This Master’s thesis therefore requires
- Expertise in graph theory,
- Interest in the structural properties of graphene, and
- mathematical writing skills (preferably also in English).
If you are interested in this work, please contact me by email. Jan Kessler and Jens M. Schmidt. Dynamics of Cycles in Polyhedra I: The Isolation Lemma. arXiv, 18.02.2020.