Nerves, minors, and piercing numbers

Andreas Holmsen

Department of Mathematical Sciences, KAIST

Department of Mathematical Sciences, KAIST

2017/5/08 Mon 4PM-5PM

We will give a topological generalization of the planar (p,q) theorem due to Alon and Kleitman. In particular we will show that the assertion of the (p,q) theorem holds for families of open connected sets in the plane under the hypothesis that the intersection of any subfamily is empty or connected. The proof is based on a surprising connection between nerve complexes and complete minors in graphs. This is join work with Minki Kim and Seunghun Lee.