Results in graph theory proved using other areas of math, and vice versa

I'm curious about learning graph theory, as it seems to pop up in some unexpected places. In order to get a partial feel for the subject, I was wondering if anyone could point me to some survey articles which focus on the interplay between graph theory and other areas of math.

Essentially, I'm looking for situations where either a result in graph theory is proved using tools previously thought to be very distant from graph theory, or a result in a field thought to be very distant from graph theory for which a graph theoretic proof exists (e.g., a proof of the Nielsen-Schreier theorem with group actions on trees).

Thanks in advance!

Solution 1:

One of my favorite "unexpected" graph theory results it's Lovász's proof of the Kneser conjecture using topological methods, particularly the Borsuk-Ulam theorem. The proof is beautiful and interesting, maybe the nicest version is the one appearing in the Proofs from THE BOOK book. There is also a great article describing the proof here.

Solution 2:

This is a really late answer, but there's a proof of the Hanna Neumann conjecture using some graph theory.