Polynomial time algorithm for the Radon number of grids in the geodetic convexity

Abstract

The Radon number of a graph is the minimum integer r such that all sets of at least r vertices of the graph can be partitioned into two subsets whose convex hulls intersect. We present a near-linear O(dlogd) time algorithm to calculate the Radon number of d-dimensional grids in the geodetic convexity. To date, no polynomial time algorithm was known for this problem.