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JCO
2016

Crossing edges and faces of line arrangements in the plane

7 years 11 months ago
Crossing edges and faces of line arrangements in the plane
For any natural number n we define f(n) to be the minimum number with the following property. Given any arrangement A(L) of n blue lines in the real projective plane one can find f(n) red lines different from the blue lines such that any edge in the arrangement A(L) is crossed by a red line. We define h(n) to be the minimum number with the following property. Given any arrangement A(L) of n blue lines in the real projective plane one can find h(n) red lines different from the blue lines such that every face in the arrangement A(L) is crossed in its interior by a red line. In this paper we show f(n) = 2n − o(n) and h(n) = n − o(n).
Rom Pinchasi
Added 06 Apr 2016
Updated 06 Apr 2016
Type Journal
Year 2016
Where JCO
Authors Rom Pinchasi
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