Shellability is hard even for balls
Abstract
The main goal of this paper is to show that shellability is NPhard for triangulated dballs (this also gives hardness for triangulated dmanifolds/dpseudomanifolds with boundary) as soon as d is at least 3. This extends our earlier work with Goaoc, Patáková and Wagner on hardness of shellability of 2complexes and answers some questions implicitly raised by Danaraj and Klee in 1978 and explicitly mentioned by SantamaríaGalvis and Woodroofe. Together with the main goal, we also prove that collapsibility is NPhard for 3complexes embeddable in the 3space, extending an earlier work of the second author and answering an open question mentioned by Cohen, Fasy, Miller, Nayyeri, Peng and Walkington; and that shellability is NPhard for 2complexes embeddable in the 3space, answering another question of SantamaríaGalvis and Woodroofe (in a slightly stronger form than what is given by the main result).
 Publication:

arXiv eprints
 Pub Date:
 November 2022
 DOI:
 10.48550/arXiv.2211.07978
 arXiv:
 arXiv:2211.07978
 Bibcode:
 2022arXiv221107978P
 Keywords:

 Computer Science  Computational Geometry;
 Mathematics  Combinatorics;
 Mathematics  Geometric Topology
 EPrint:
 66 pages, 51 figures (The figures take nontrivial portion of the space thus in reality the paper is a bit shorter.)