TY - CONF
AB - 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.
AU - Goaoc, Xavier
AU - Paták, Pavel
AU - Patakova, Zuzana
AU - Tancer, Martin
AU - Wagner, Uli
ID - 184
TI - Shellability is NP-complete
VL - 99
ER -