Colouring criteria for adjacency on 0–1-polyhedra

The adjacency of two vertices on an arbitrary 0–1-polyhedron P is characterized by certain criteria involving the (prime) implicants of P, which are generalizations of the circuits of an independence system. These criteria can be checked by straightforward “colouring algorithms”. They are sufficient for all 0–1-polyhedra and necessary for at least three classes containing the polyhedra of many well-known discrete optimization problems, e.g. the vertex packing problem, set packing problem, vertex covering problem, matching problem, assignment problem, partitioning problem, linear ordering problem, partial ordering problem.