Planar Cayley graphs
Agelos Georgakopoulos, TU Graz

In this talk I will present a classification of the cubic planar (mostly infinite) Cayley graphs. This turns out to be a very rich class of graphs, comprising 36 infinite families and one sporadic element, and containing surprising examples contradicting earlier beliefs.

It turns out that there is an effective enumeration of these graphs, confirming a conjecture of Droms et. al., and each element is effectively computable.

This classification implies refinements of Stallings' celebrated theorem for these graphs. I conjecture that such refinements are possible in general.

I will assume no prerequisites, but it would be good to know what a Cayley graph is. There will be many pictures.