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).