(See also my preprints.)
Citation counts are taken from Google Scholar, which on occasion overcounts slightly.
There was an error in our original proof of Lemma 3.4 in the paper, as was pointed out by Fahimeh Khosh-Ahang and Somayeh Moradi in this arXiv preprint. A corrected proof is in the corrigendum published here. (It is also attached at the end of the arXiv version of the paper.) We are grateful to Khosh-Ahang and Moradi for bringing the error to our attention.
At the end of Section 6, the direct product of two edges is shellable. The direct product of an edge and a 3-cycle is bipartite, and is not shellable or sCM, but is not K3,3. I thank Sara Saeedi for pointing out my mistake.
The history of shelling in this paper is incomplete: the idea of shellability goes back considerably before Bruggesser and Mani. Even the term shelling goes back at least to DE Sanderson's 1957 paper Isotopy in 3-Manifolds I. Isotopic Deformations of 2-Cells and 3-Cells. RH Bing discusses shellings at some length in his 1964 book Some aspects of the topology of 3-manifolds related to the Poincaré conjecture.
Günter Ziegler's paper Shelling Polyhedral 3-Balls and 4-Polytopes has a nice discussion of the history of nonshellable balls.
A simpler construction of an EL-labeling for the coset lattice of a complemented group is in Section 4.2 of my paper Cubical convex ear decompositions. See above.