Polyhedral aspects of transportation problems

This note announces several recent results on the polyhedral combinatorics of transportation problems: the solution of the maximal diameter conjecture for the case of a G-truncated transportation polyhedron (TP), the determination of attainable lower and upper bounds for the diameter and radius in the class of G-truncated TP’s with a given number of faces, the criterion for a polyhedron to belong to the class of symmetrical TP’s with maximal number of vertices, and the solution of Dubois’ conjecture on the maximal number of vertices.