On the hypergraph connectivity of skeleta of polytopes

Abstract

We show that for every $d$-dimensional polytope, the hypergraph whose nodes are $k$-faces and whose hyperedges are $(k+1)$-faces of the polytope is strongly $(d-k)$-vertex connected, for each $0\le k\le d-1$.

3 pages, LaTeX; typos corrected, exposition clarified