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empty triangle
Monochromatic empty triangles โ โ โ
Author(s):
If is a finite set of points which is 2-colored, an empty triangle is a set
with
so that the convex hull of
is disjoint from
. We say that
is monochromatic if all points in
are the same color.
Conjecture There exists a fixed constant
with the following property. If
is a set of
points in general position which is 2-colored, then it has
monochromatic empty triangles.
![$ c $](/files/tex/dccee841f3f498c2c58fa6ae1c1403c5a88c5b8d.png)
![$ X \subseteq {\mathbb R}^2 $](/files/tex/71fbba54c5abad01c67f2c62eac8eb5eb7b71842.png)
![$ n $](/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png)
![$ \ge cn^2 $](/files/tex/7cb1c285388b3509a0bafac8c671235c0a740e56.png)
Keywords: empty triangle; general position; ramsey theory
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