preprint
Hereditary-shellable simplicial complexes.
by Masahiro Hachimori and Kenji Kashiwabara
Abstract
Hereditary-shellable simplicial complexes are those such that any restrictions,
including themselves, are shellable. Matroid complexes are examples of
hereditary-shellable simplicial complexes.
We show that the pure 2-skeletons of 2-dimensional hereditary-shellable simplicial
complexes are extendably shellable. This generalizes the result of Bjorner and Eriksson
that matroid complexes of dimension 2 are extendably shellable. On the other hand,
we give an example of a 2-dimensional hereditary-shellable simplicial complex that
is not vertex decomposable. Further, we discuss properties of pure skeletons of strong
obstructions to shellability as an application of our result.