Martin Tancer: d-collapsibility is NP-complete for d greater or equal to 4

Abstract: A simplicial complex is d-collapsible if it can be reduced to an empty complex by repeatedly removing (collapsing) a face of dimension at most d-1 that is contained in a unique maximal face. We prove that the algorithmic question whether a given simplicial complex is d-collapsible is NP-complete for d greater or equal to 4 and polynomial time solvable for d at most 2. As an intermediate step, we prove that d-collapsibility can be recognized by the greedy algorithm for d at most 2, but the greedy algorithm does not work for d greater or equal 3.