Discrete Mathematics, 308 (2008), 2307-2312.
Decompositions of two-dimensional simplicial complexes.
by Masahiro Hachimori
Abstract
We show that the class of Cohen-Macaulay complexes, that of complexes
with constructible subdivisions,
and that of complexes with shellable subdivisions
differ from each other in every dimension $d \ge 2$.
Further, we give a characterization of $2$-dimensional simplicial complexes
with shellable subdivisions, and show also that they are constructible.