Balanced lines in two–coloured point sets
نویسندگان
چکیده
Let B and R be point sets (of blue and red points, respectively) in the plane, such that P := B ∪R is in general position, and |P | is even. A line l is balanced if it spans one blue and one red point, and on each open halfplane of l, the number of blue points minus the number of red points is the same. We prove that P has at least min{|B|, |R|} balanced lines. This refines a result by Pach and Pinchasi, who proved this for the case |B| = |R|.
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