# Proofs of circle packing theorem

Circle packing theorem is a famous result stating that for every connected simple planar graph $$G$$ there is a circle packing in the plane whose intersection graph is $$G$$ https://en.wikipedia.org/wiki/Circle_packing_theorem.

I know that this result has many proofs and I want to read one of them, but don't understand how to start (for quite a while). The article in wiki gives a reference to Thurston notes, but the proof comes only in the last section and I am not sure if this is the simplest approach. I like these notes very much, but was never able to read them till the end. So I wonder if there are some simple proofs of this result nowadays. Can you advise something?

• may be the fact that there exists a triangulation of every maximal planar graph may come handy in the proof – vidyarthi Aug 25 '20 at 10:28
• Does this answer to your question?mathoverflow.net/q/187845/90655 – C.F.G Sep 3 '20 at 8:23
• Thanks a lot C.F.G! I have not spotted this question. It looks like mine is a duplicate. I'll study the answers – aglearner Sep 3 '20 at 13:39
• Although your question is close to a duplicate to "Koebe–Andreev–Thurston theorem - where can I find a proof?," additional expositions have appeared in the ~6 yrs since that post. – Joseph O'Rourke Sep 3 '20 at 17:26