Collapsibility of simplicial complexes of hypergraphs

Abstract

Let $\mathcal{H}$ be a hypergraph of rank $r$. We show that the simplicial complex whose simplices are the hypergraphs $\mathcal{F}\subset \mathcal{H}$ with covering number at most $p$ is $\left(\left(\genfrac{}{}{0ex}{}{r+p}{r}\right)-1\right)$-collapsible, and the simplicial complex whose simplices are the pairwise intersecting hypergraphs $\mathcal{F}\subset \mathcal{H}$ is $\frac{1}{2}\left(\genfrac{}{}{0ex}{}{2r}{r}\right)$-collapsible.