Polybasic polyhedra: Structure of polyhedra with edge vectors of support size at most 2 (Q1827668)

The concept of base polyhedra associated with submodular functions in combinatorial optimization [see the first author's book Submodular functions and optimization (Amsterdam etc.: North-Holland) (1991; Zbl 0728.90056)] is extended to polybasic polyhedra and some characterzations of such polyhedra are given. A polybasic polyhedron is a pointed convex polyhedron in \(\mathbb R^V\) whose edge vectors have support size at most 2, where \(V\) is a finite set. This new class of polyhedra includes base polyhedra, submodular polyhedra, generalized polymatroids, etc.