Abstract
Given a set of n black and n white points in general position in the plane, a line l determined by them is said to be balanced if each open half-plane bounded by l contains precisely the same number of black points as white points. It is proved that the number of balanced lines is at least n . This settles a conjecture of George Baloglou.
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Received August 1, 2000, and in revised form October 23, 2000. Online publication April 6, 2001.
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Pach, J., Pinchasi, R. On the Number of Balanced Lines. Discrete Comput Geom 25, 611–628 (2001). https://doi.org/10.1007/s00454-001-0013-3
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DOI: https://doi.org/10.1007/s00454-001-0013-3