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Journal Articles Journal of the ACM (JACM) Year : 2019

Shellability is NP-complete


We prove that for every $d\geq 2$, 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 $d \ge 2$ and $k \ge 0$, deciding if a pure, $d$-dimensional, simplicial complex is $k$-decomposable is NP-hard. For $d \ge 3$, both problems remain NP-hard when restricted to contractible pure $d$-dimensional complexes. Another simple corollary of our result is that it is NP-hard to decide whether a given poset is CL-shellable.

Dates and versions

hal-02050505 , version 1 (27-02-2019)



Xavier Goaoc, Pavel Paták, Zuzana Patáková, Martin Tancer, Uli Wagner. Shellability is NP-complete. Journal of the ACM (JACM), 2019, 66 (3), pp.1-18. ⟨10.1145/3314024⟩. ⟨hal-02050505⟩
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