Publication at Faculty of Mathematics and Physics |
2009
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 }= 4 and polynomial time solvable for d {= 2.
As an intermediate step, we prove that d-collapsibility can be recognized by the greedy algorithm for d {= 2, but the greedy algorithm does not work for d }= 3.