A new $k$-partite graph $k$-clique iterator and the optimal colored Tverberg problem for ten colored points

Abstract

We provide an algorithm that verifies the optimal colored Tverberg problem for $10$ points in the plane: Every $10$ points in the plane in color classes of size at most $3$ can be partitioned in $4$ rainbow pieces such that their convex hulls intersect in a common point. This is achieved by translating the problem to $k$-partite graphs and using a new algorithm to verify that those graphs do not have a $k$-clique.

17 pages, 5 figures, 7 tables