Contact graphs of totally separable packings
Konrad SwanepoelBBC+G Seminar
on 10/19/23
Let A,B be two families of vectors in R^d that both span it and such that is either 0 or 1 for any a, b from A and B, respectively. We show that . This allows us to settle a conjecture by Bohn, Faenza, Fiorini, Fisikopoulos, Macchia, and Pashkovich (2015) concerning 2-level polytopes (polytopes such that for every facet-defining hyperplane H there is its translate H' such that H together with H' cover all vertices). The authors conjectured that for every d-dimensional 2-level polytope P the product of the number of vertices of P and the number of facets of P is at most , which we show to be true. Joint work with Stefan Weltge.