Collapsibility to a subcomplex of a given dimension is NPcomplete
Abstract
In this paper we extend the works of Tancer and of Malgouyres and Francés, showing that $(d,k)$collapsibility is NPcomplete for $d\geq k+2$ except $(2,0)$. By $(d,k)$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 $(d,k)$collapsibility was asked by Tancer, who proved NPcompleteness of $(d,0)$ and $(d,1)$collapsibility (for $d\geq 3$). Our extended result, together with the known polynomialtime algorithms for $(2,0)$ and $d=k+1$, answers the question completely.
 Publication:

arXiv eprints
 Pub Date:
 March 2017
 arXiv:
 arXiv:1703.06983
 Bibcode:
 2017arXiv170306983P
 Keywords:

 Computer Science  Computational Geometry;
 Computer Science  Computational Complexity;
 Mathematics  Geometric Topology
 EPrint:
 Discrete &