Disjoint non-monochromatic triangles in the plane
Andreas F. Holmsen, Claudiu Valculescu · arXiv (Cornell University) · 2016
Let R and B be two disjoint sets of points in the plane, such that |R|+|B| is a multiple of 3, and the set $ R\cup B $ is in general position. We say that a triangle is non-monochromatic if its vertices are from $ R\cup B $, and it has at least one vertex from R, and at least one vertex from B. We prove that one can split the set $ R\cup B $ into n disjoint non-monochromatic triangles. Our result is in the spirit of a recent result of Kano and Kyncl, but our proof uses elementary tools and avoids approximation in limit. We also put the problem into a more general context and discuss possible extensions of our result.