Disjoint tree-compatible plane perfect matchings
O. Aichholzer, J. Obmann, P. Patak, D. Perz, J. Tkadlec, in:, 36th European Workshop on Computational Geometry, 2020.

Shellability is NP-complete
X. Goaoc, P. Patak, Z. Patakova, M. Tancer, U. Wagner, Journal of the ACM 66 (2019).