Convex sets assigned to a triangulation
Source: Miklós Schweitzer 2014, problem 10
December 23, 2014
geometry3D geometryspheregeometry unsolved
Problem Statement
To each vertex of a given triangulation of the two-dimensional sphere, we assign a convex subset of the plane. Assume that the three convex sets corresponding to the three vertices of any two-dimensional face of the triangulation have at least one point in common. Show that there exist four vertices such that the corresponding convex sets have at least one point in common.