Shellability is NP-complete

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Shellability is NP-complete

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...

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ژورنال

عنوان ژورنال: Journal of the ACM

سال: 2019

ISSN: 0004-5411,1557-735X

DOI: 10.1145/3314024