Balanced line for a 3colored 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 halfplane bounded by
l contains exactly k red, k blue and k green points for some k ∈ {1,2,..,n1}.
We prove that a balanced line exists if the convex hull of S is monochromatic.
Balanced line for a set of 18 points.


@article{bkbl3ps12
, author = {Sergey Bereg and Mikio Kano}
, title = {Balanced line for a 3colored point set in the plane}
, journal = {the Electronic Journal of Combinatorics}
, year = {2012}
, note = {to appear}
}
