Characterization of the types of maximum noninteger vertices in the relaxation polyhedron of the four-index axial assignment problem

For the relaxation polyhedron M(4, n) in the four-index axial assignment problem of order n, n ≥ 3, a characterization of all possible types (except for a single case) of maximum noninteger vertices, i.e., vertices with 4n — 3 fractional components is proposed. A formula enumerating all the maximum noninteger vertices of the same type in M(4, n) is derived.