Separation by Convex Pseudo-Circles
Nicolas Chevallier, Augustin Fruchard, Dominique Schmitt, Jean-Claude Spehner · 2014
Let S be a finite set of n points in the plane in general position. We prove that every inclusion-maximal family of subsets of S separable by convex pseudo-circles has the same cardinal (n 0)+(n 1)+(n 2)+(n 3). This number does not depend on the configuration of S and is the same as the number of subsets of S separable by true circles. Buzaglo, Holzman, and Pinchasi already showed that it is an upper bound for the number of subsets separable by (non necessarily convex) pseudo-circles.