The pure-EKR conjecture for flag pseudo-manifolds

A simplicial complex is pure-EKR if its facets have the Erdős–Ko–Rado property. A pure simplicial complex is a pseudo-manifold if every ridge, meaning every codimension-one face, is contained in exactly two facets; it is flag if every set of pairwise adjacent vertices forms a face.

Flag pseudo-manifold conjecture. Every flag pseudo-manifold is pure-EKR.

Every simplicial manifold is a weak pseudo-manifold, so this conjecture generalizes the flag-manifold conjecture and the polygon-triangulation case. It is not settled in arbitrary dimension.