Hereditary-shellable simplicial complexes.

by Masahiro Hachimori and Kenji Kashiwabara


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.