A conjecture of Branko Grünbaum from 1972 states that any simple arrangement of n pairwise intersecting pseudocircles in the plane can have at most 2n-2 digons. We will present a solution of Grünbaum's Conjecture in the special case of pairwise intersecting geometric circles. In the remaining time we will sketch the solution of Grünbaum’s Conjecture in full generality for pseudocircles. The general solution is independent of the solution for the case of circles, but it uses an abstract idea from the proof for circles, without which the proof of the general case of Grünbaum's Conjecture could not be carried out.

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This is a joint work with Eyal Ackerman, Gabor Damasdi, Balazs Keszegh, and Rebeka Raffay