The Isolation Lemma – Longest Circles in Planar Graphs

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 [1] 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.

[1] Jan Kessler and Jens M. Schmidt. Dynamics of Cycles in Polyhedra I: The Isolation Lemma. arXiv, 18.02.2020.