Interactions between geometry and graph theory.

Question

I'm looking for some nice theories or just exercises, with both geometrical aspects and graph theoretics aspects.

Example may include for instance the 4-color theorem or Euler characteristics, maybe Königsberg's bridges (although this last one is almost purely graph theoretic). Ideally I'm looking for material that is not too advanced, like first year of university.

Answer 1

Oriented matroids may be a link between geometry and graph theory.