Abstract
Continuing and extending the analysis in a previous paper [15], we establish several combinatorial results on the complexity of arrangements of circles in the plane. The main results are a collection of partial solutions to the conjecture that (a) any arrangement of unit circles with at least one intersecting pair has a vertex incident to at most three circles, and (b) any arrangement of circles of arbitrary radii with at least one intersecting pair has a vertex incident to at most three circles, under appropriate assumptions on the number of intersecting pairs of circles (see below for a more precise statement).
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Received June 26, 2000, and in revised form January 30, 2001. Online publication October 5, 2001.
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Alon, N., Last, H., Pinchasi, R. et al. On the Complexity of Arrangements of Circles in the Plane. Discrete Comput Geom 26, 465–492 (2001). https://doi.org/10.1007/s00454-001-0043-x
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DOI: https://doi.org/10.1007/s00454-001-0043-x