License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.SoCG.2018.41
URN: urn:nbn:de:0030-drops-87542
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Goaoc, Xavier ; Paták, Pavel ; Patáková, Zuzana ; Tancer, Martin ; Wagner, Uli

Shellability is NP-Complete

LIPIcs-SoCG-2018-41.pdf (0.7 MB)


We prove that for every d >= 2, deciding if a pure, d-dimensional, simplicial complex is shellable is NP-hard, hence NP-complete. This resolves a question raised, e.g., by Danaraj and Klee in 1978. Our reduction also yields that for every d >= 2 and k >= 0, deciding if a pure, d-dimensional, simplicial complex is k-decomposable is NP-hard. For d >= 3, both problems remain NP-hard when restricted to contractible pure d-dimensional complexes.

BibTeX - Entry

  author =	{Xavier Goaoc and Pavel Pat{\'a}k and Zuzana Pat{\'a}kov{\'a} and Martin Tancer and Uli Wagner},
  title =	{{Shellability is NP-Complete}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{41:1--41:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Bettina Speckmann and Csaba D. T{\'o}th},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-87542},
  doi =		{10.4230/LIPIcs.SoCG.2018.41},
  annote =	{Keywords: Shellability, simplicial complexes, NP-completeness, collapsibility}

Keywords: Shellability, simplicial complexes, NP-completeness, collapsibility
Collection: 34th International Symposium on Computational Geometry (SoCG 2018)
Issue Date: 2018
Date of publication: 08.06.2018

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