Abstract
We show that n arbitrary circles in the plane can be cut into O(n 3/2+ɛ ) arcs, for any ɛ>0 , such that any pair of arcs intersects at most once. This improves a recent result of Tamaki and Tokuyama [20]. We use this result to obtain improved upper bounds on the number of incidences between m points and n circles. An improved incidence bound is also obtained for graphs of polynomials of any constant maximum degree.
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Aronov, Sharir Cutting Circles into Pseudo-Segments and Improved Bounds for Incidences% and Complexity of Many Faces. Discrete Comput Geom 28, 475–490 (2002). https://doi.org/10.1007/s00454-001-0084-1
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DOI: https://doi.org/10.1007/s00454-001-0084-1