Decompositions, Shellings, and Diameters of Simplicial Complexes and Convex Polyhedra.

摘要

Simplicial complexes are studied in their role dual to convex polyhedra, in particular, with respect to shellability and diameters. The concept of k-decomposability is presented which both insures shellability and limits the diameter of a simplicial complex. k-decomposability is studied in relation to standard techniques used in polyhedral theory, and with respect to topological properties of simplicial complexes. (Author)