Circle packing theorem: For every connected simple planar graph G there is a circle packing in the plane whose intersection graph is (isomorphic to) G.
Read more about Circle Packing Theorem: A Uniqueness Statement, Generalizations of The Circle Packing Theorem, Relations With Conformal Mapping Theory, Applications of The Circle Packing Theorem, Proofs of The Theorem, Implications, Algorithmic Aspects, History
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