Shellability is NP-complete

11/22/2017

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by   Xavier Goaoc, et al.

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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.