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Communication Dans Un Congrès Année : 2018

Shellability is NP-complete

Résumé

We prove that for every $d\geq 2$, deciding if a pure, $d$-dimensional, simplicial complex is shellable is \textup{NP}-hard, hence \textup{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 \textup{NP}-hard. For $d \ge 3$, both problems remain \textup{NP}-hard when restricted to contractible pure $d$-dimensional complexes.

Dates et versions

hal-01744101 , version 1 (27-03-2018)

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Xavier Goaoc, Pavel Paták, Zuzana Patáková, Martin Tancer, Uli Wagner. Shellability is NP-complete. International Symposium on Computational Geometry, 2018, Budapest, Hungary. ⟨10.4230/LIPIcs.SoCG.2018.41⟩. ⟨hal-01744101⟩
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