Geodesic
Balanced line for a 3-colored point set in the plane
The electronic journal of combinatorics, Tome 19 (2012) no. 1
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In this note we prove the following theorem. For any three sets of points in the plane, each of $n\ge 2$ points such that any three points (from the union of three sets) are not collinear and the convex hull of $3n$ points is monochromatic, there exists an integer $k\in\{1,2,\dots,n-1\}$ and an open half-plane containing exactly $k$ points from each set.
DOI : 10.37236/2037
Classification : 52A37 
@article{10_37236_2037,
     author = {Sergey Bereg and Mikio Kano},
     title = {Balanced line for a 3-colored point set in the plane},
     journal = {The electronic journal of combinatorics},
     year = {2012},
     volume = {19},
     number = {1},
     doi = {10.37236/2037},
     zbl = {1246.52011},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2037/}
}
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Sergey Bereg; Mikio Kano. Balanced line for a 3-colored point set in the plane. The electronic journal of combinatorics, Tome 19 (2012) no. 1. doi: 10.37236/2037

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