Discrete Math Seminar

Hadwiger's transversal theorem gives necessary and sufficient conditions for the existence of a line transversal to a family of pairwise disjoint convex sets in the plane. These conditions were subsequently generalized to hyperplane transversals in ${\mathbb{R}}^d$ by Goodman, Pollack, and Wenger. Here we establish a colorful extension of their theorem, which proves a conjecture of …