I would appreciate if anyone could help me with the following problem:
Given a set of 3n points in the plane with n > 0, is it possible to find a placement of a tripod such that each region contains at most n of the points?
If it is possible, then can we prove that a valid placement always exists?
If it is not possible, then can anyone provide me a set of 3n points (with n > 0) and a tripod T and prove that there is no placement of T which has the required properties.
Here, I am considering the points in general position, i.e. no three points are collinear. Also by my understanding, tripod is a point (say p) with three rays emanating from p such that the angle between two consecutive rays is 2π/3 (120 degree). Also the tripod can partition the plane into three regions(i.e. cones).