Collapsibility of Simplicial Complexes of Hypergraphs

Alan Lew
2019 Electronic Journal of Combinatorics  
Let $\mathcal{H}$ be an $r$-uniform hypergraph. We show that the simplicial complex whose simplices are the hypergraphs $\mathcal{F}\subset\mathcal{H}$ with covering number at most $p$ is $\left(\binom{r+p}{r}-1\right)$-collapsible. Similarly, the simplicial complex whose simplices are the pairwise intersecting hypergraphs $\mathcal{F}\subset\mathcal{H}$ is $\frac{1}{2}\binom{2r}{r}$-collapsible.
doi:10.37236/8364 fatcat:rmzieflcubfurkrnj6pq6wc5cy