Large Bichromatic Point Sets Admit Empty Monochromatic 4-Gons

@article{Aichholzer2010LargeBP,
  title={Large Bichromatic Point Sets Admit Empty Monochromatic 4-Gons},
  author={Oswin Aichholzer and Thomas Hackl and Clemens Huemer and Ferran Hurtado and Birgit Vogtenhuber},
  journal={SIAM J. Discrete Math.},
  year={2010},
  volume={23},
  pages={2147-2155}
}
We consider a variation of a problem stated by Erdős and Szekeres in 1935 about the existence of a number f(k) such that any set S of at least f(k) points in general position in the plane has a subset of k points that are the vertices of a convex k-gon. In our setting the points of S are colored, and we say that a (not necessarily convex) spanned polygon is monochromatic if all its vertices have the same color. Moreover, a polygon is called empty if it does not contain any points of S in its… CONTINUE READING