Balanced line for a 3-colored point set in the plane

by Sergey Bereg and Mikio Kano

Abstract: In this note we study balanced lines for three point sets. Let S=R ∪ B ∪ G be a set of 3n points in the plane in general position such that |R|=|B|=|G|=n>=2 (red, blue and green points). A line l is called balanced if an open half-plane bounded by l contains exactly k red, k blue and k green points for some k ∈ {1,2,..,n-1}. We prove that a balanced line exists if the convex hull of S is monochromatic.
A balanced line for a set of 18 points.

, author = {Sergey Bereg and Mikio Kano}
, title = {Balanced line for a 3-colored point set in the plane}
, journal = {the Electronic Journal of Combinatorics}
, volume = {19}
, pages = {P33}
, year = {2012}