# Collapsibility to a Subcomplex of a Given Dimension is NP-Complete

@article{Paolini2017CollapsibilityTA, title={Collapsibility to a Subcomplex of a Given Dimension is NP-Complete}, author={Giovanni Paolini}, journal={Discrete & Computational Geometry}, year={2017}, volume={59}, pages={246-251} }

In this paper we extend the works of Tancer, Malgouyres and Francés, showing that $$(d,k)$$(d,k)-Collapsibility is NP-complete for $$d\ge k+2$$d≥k+2 except (2, 0). By $$(d,k)$$(d,k)-Collapsibility we mean the following problem: determine whether a given d-dimensional simplicial complex can be collapsed to some k-dimensional subcomplex. The question of establishing the complexity status of $$(d,k)$$(d,k)-Collapsibility was asked by Tancer, who proved NP-completeness of (d, 0) and $$(d,1)$$(d,1… CONTINUE READING

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