Convex decompositions of polyhedra

We introduce the property of k-decomposability for simplicial complexes which, if satisfied by the dual simplicial complex of a convex polyhedron, implies that the diameter of the polyhedron is bounded by a polynomial of degree k + 1 in the number of ...

We characterize the convex polyhedra P in $${\mathbb {R}}^n$$Rn for which any family of n-dimensional axis-parallel hypercubes centered in P and intersected with P has the binary intersection property. The characterization is effective, concrete and ...

Adjacency properties of extreme points of a convex polyhedron are discussed. In mathematical programming we are quite often faced with problems of characterizing the extreme points of a convex polyhedron of the form $K \cap H$ or $K \cap L$, where $K \...