Ariadna Olvera-Sampieri

Pushed colorful polytopal KKMS Theorem and orthogonal star transversals

A classical theorem of Kaiser and Rabinovich implies that if every subfamily of size at most $\lfloor\log_2(d+1)\rfloor+1$ of a finite family of compact connected sets in $\mathbb{R}^d$ has a common axis-parallel hyperplane transversal, then the entire family has an orthogonal star transversal, i.e., a union of $d$ hyp...