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.
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@article{bk-bl3ps-12
, 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}
}
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