volume 28, issue 4, P475-490 2002
DOI: 10.1007/s00454-001-0084-1
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## Abstract: We show that n arbitrary circles in the plane can be cut into O(n 3/2+ε ) arcs, for any ε > 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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